The International Linear Collider: A Global Project
Philip Bambade, Tim Barklow, Ties Behnke, Mikael Berggren, James Brau, Philip Burrows, Dmitri Denisov, Angeles Faus-Golfe, Brian Foster, Keisuke Fujii, Juan Fuster, Frank Gaede, Paul Grannis, Christophe Grojean, Andrew Hutton, Benno List, Jenny List, Shinichiro Michizono, Akiya Miyamoto, Olivier Napoly, Michael Peskin, Roman Poeschl, Frank Simon, Jan Strube, Junping Tian, Maksym Titov, Marcel Vos, Andrew White, Graham Wilson, Akira Yamamoto, Hitoshi Yamamoto, Kaoru Yokoya
DDESY 19-037, FERMILAB-FN-1067-PPD, IFIC/19-10IRFU-19-10, JLAB-PHY-19-2854, KEK Preprint 2018-92LAL/RT 19-001, PNNL-SA-142168, SLAC-PUB-17412March 2019
The International Linear ColliderA Global Project
Prepared by:
Philip Bambade , Tim Barklow , Ties Behnke , Mikael Berggren , James Brau , Philip Burrows ,Dmitri Denisov , , Angeles Faus-Golfe , Brian Foster , , Keisuke Fujii , Juan Fuster , Frank Gaede , Paul Grannis ,Christophe Grojean , Andrew Hutton , Benno List , Jenny List , Shinichiro Michizono , Akiya Miyamoto , OlivierNapoly , Michael Peskin , Roman P¨oschl , Frank Simon , Jan Strube , , Junping Tian , Maksym Titov ,Marcel Vos , Andrew White , Graham Wilson , Akira Yamamoto , Hitoshi Yamamoto , Kaoru Yokoya LAL-Orsay/CNRS, SLAC, DESY, U. Oregon, Oxford U., BNL, Fermilab, KEK, IFIC, U. Valencia-CSIC, Stony Brook U., Jefferson Lab, IRFU, CEA Saclay, Max Planck Inst., Munich, PNNL, U. Tokyo, U. Texas, Arlington, U. Kansas, U. Tohoku (Representing the Linear Collider Collaboration and the global ILC community.)
The International Linear Collider (ILC) is now under consideration as the next global project inparticle physics. In this report, we review of all aspects of the ILC program: the physics motivation,the accelerator design, the run plan, the proposed detectors, the experimental measurements on theHiggs boson, the top quark, the couplings of the W and Z bosons, and searches for new particles. Wereview the important role that polarized beams play in the ILC program. The first stage of the ILCis planned to be a Higgs factory at 250 GeV in the centre of mass. Energy upgrades can naturallybe implemented based on the concept of a linear collider. We discuss in detail the ILC program ofHiggs boson measurements and the expected precision in the determination of Higgs couplings. Wecompare the ILC capabilities to those of the HL-LHC and to those of other proposed e + e − Higgsfactories. We emphasize throughout that the readiness of the accelerator and the estimates of ILCperformance are based on detailed simulations backed by extensive R&D and, for the acceleratortechnology, operational experience.
CONTENTS
1. Introduction 32. ILC Machine Design 52.1. Design evolution since the TDR 62.2. Superconducting RF Technology 82.2.1. The quest for high gradients 82.2.2. Further cost reduction R&D 112.2.3. Basic parameters 112.2.4. Cavities 122.2.5. Power coupler 122.2.6. Cryomodules 132.2.7. Plug-compatible design 132.2.8. High-level radio-frequency 132.2.9. Cryogenics 142.2.10. Series production andindustrialisation, worldwide and inEurope 142.3. Accelerator design 152.3.1. Electron and positron sources 152.3.2. Damping rings 162.3.3. Low emittance beam transport: ringto Main Linac (RTML) 172.3.4. Bunch compressors and MainLinac 17 2.3.5. Beam delivery system and machinedetector interface 182.4. Upgrade options 212.4.1. Energy upgrade 212.4.2. Luminosity upgrade 212.4.3. Polarisation upgrade 222.5. Civil engineering and site 222.6. Cost and schedule 223. ILC Running Scenarios 233.1. Center-of-mass energies and integratedluminosities 243.2. Beam polarisation 253.3. Time evolution and upgrade options 263.3.1. Running scenarios for the 500-GeVMachine 263.3.2. Running scenarios for the stagedmachine 274. Physics Case – 250 GeV 284.1. Mysteries of the Higgs boson 294.2. Examples of new physics influence on theHiggs boson 294.3. Limitations of the LHC measurements onthe Higgs boson 304.4. e + e − → ZH a r X i v : . [ h e p - e x ] A p r e + e − → W + W − e + e − → f f e + e − reactions 375.5. Direct searches for physics beyond theStandard Model 376. Detectors 386.1. Introduction 386.2. The SiD detector 386.2.1. Silicon-based tracking 396.2.2. Vertex detector 396.2.3. Main tracker 406.2.4. Main calorimeters 416.2.5. Forward calorimeters 426.2.6. Magnet coil 426.2.7. Muon system 426.2.8. The machine-detector interface 426.3. The ILD detector 426.3.1. Vertexing and tracking 436.3.2. Calorimetry 436.3.3. Coil and yoke 446.3.4. Detector integration andperformance 447. Computing, Event Reconstruction, and DetectorPerformance 447.1. Core software tools 447.2. Event generators 457.3. Simulation 467.4. Digitzation 467.5. Reconstruction 477.5.1. Tracking 477.5.2. Particle Flow: 487.6. High-level reconstruction 507.7. Fast simulation 507.8. Computing concept 517.9. Computing resource estimate 518. Physics Simulations: Higgs 518.1. Common procedures for event selections 548.2. Analyses for Higgs observables 558.2.1. m h and σ Zh σ ννh and σ eeh h → bb/cc/gg ) 588.2.4. BR( h → W W ∗ /ZZ ∗ ) 598.2.5. BR( h → τ + τ − ) 608.2.6. BR( h → invisible / exotic) 608.2.7. BR( h → µ + µ − /γγ/γZ ) 61 8.2.8. Higgs CP properties 618.2.9. Angular analyses for anomalous HV V couplings 618.3. Systematic uncertainties, and theimportance of beam polarisation 618.3.1. Systematic uncertainties consideredin the Higgs coupling fit 628.3.2. Control of systematic uncertaintiesusing beam polarisation 638.4. Estimation of future improvements 658.5. Measurement of the Higgs bosonself-coupling 659. Physics Simulations: Electroweak Production of2- and 4-Fermion Final States 679.1. Analyses of e + e − → W + W − W mass measurement at 250 GeV 699.2. Analyses of e + e − → f f e + e − → f f analyses 719.2.3. e + e − → τ + τ − e + e − → bb e + e − Higgs factoryproposals 8011.3. Comparison of the ILC and the HL-LHCHiggs capabilities 8012. Physics Simulations: Direct Searches for NewParticles 8412.1. Pair-production signatures 8612.1.1. Loop-hole free searches 8712.1.2. Sleptons 8812.1.3. Bosinos 8912.1.4. Small mass differences 9012.2. Mono-photon signature 9212.3. New-scalar signatures 9313. Conclusion 94References 96
1. INTRODUCTION
While the Standard Model (SM) is a highly success-ful theory of the fundamental interactions, it has se-rious shortcomings. New fundamental interactions arerequired to address them. A central focus of particlephysics now involves searching for these new interactionsand associated new particles. The SM is theoreticallyself-consistent, but it does not answer many obvious ques-tions about particle physics. It has no explanation for thedark matter or dark energy that is observed in the cos-mos, or for the cosmic excess of matter over antimatter.It does not address the mass scale of quarks, leptons,and gauge bosons, which is significantly lower than thePlanck scale. It does not explain the large mass ratiosamong the SM particles or the values of the quark andneutrino mixing angles. These and other considerationsprovide a compelling motivation for new interactions be-yond the SM. On the other hand, the current success ofthe SM indicates that further search will be very chal-lenging and, most likely, requires new approaches andnew methods.The discovery of the Higgs boson in 2012 revealed thefinal particle predicted in the SM. Within that theory,the Higgs boson is the agent for electroweak symmetrybreaking and the generation of the masses of all elemen-tary particles. Thus, it occupies a central role in the SMand, specifically, in many of the unresolved issues that wehave listed above. The properties of the Higgs boson areprecisely specified in the SM, while models of new inter-actions that address these issues lead to significant cor-rections to those predictions. Thus, high-precision mea-surement of the Higgs boson offers a new and promisingavenue for searches for new physics beyond the StandardModel. The discovery of deviations of the Higgs bosonproperties from the SM predictions could well providethe first evidence for new physics beyond the SM.This study of the Higgs boson properties is themost prominent goal of the International Linear Collider(ILC). The ILC has been designed with this goal in mind,to provide a complete, high-precision picture of the Higgsboson and its interactions. Though the properties ofthe Higgs boson are already being studied at the LHC,the ILC offers significant advantages. It will bring themeasurements to a new, qualitatively superior, level ofprecision, and it will remove the many model-dependentassumptions required for the analysis of the Higgs bo-son measurements at hadron colliders. The ILC will behighly sensitive to Higgs boson decays that yield invisibleor other exotic final states, giving unique tests of mod-els of new weakly interacting particles and dark matter.The ILC can also probe for direct pair-production of par-ticles with very weak interactions. Since direct searchesat high-energy hadron colliders have not discovered newparticles, it is urgent and compelling to open this newpath to the search for physics beyond the SM.As an e + e − linear collider, the ILC brings a number ofvery powerful experimental tools to bear on the challenge of producing a precise, model-independent accounting ofthe Higgs boson properties. The ILC has a well-defined,adjustable centre-of-mass energy. It produces conven-tional SM events at a level that is comparable to, ratherthan overwhelmingly larger than, Higgs signal processes,allowing easy selection of Higgs boson events. At its ini-tial stage of 250 GeV, Higgs boson events are explicitlytagged by a recoil Z boson. At a linear collider, boththe electron and positron beams can be polarized, intro-ducing additional observables. Because all electroweakreactions at energies above the Z resonance have order-1parity violation, beam polarization effects are large andprovide access to critical physics information.After operation of a linear collider at the starting en-ergy, it is straightforward to upgrade the centre-of-massenergy. This is the natural path of evolution for a newhigh-energy physics laboratory. An upgrade in energysystematically expands the list of physics processes thatcan be studied with high precision and polarized beams.An upgrade to 500 GeV accesses the Higgs boson cou-pling to the top quark and the Higgs boson self-coupling.Together with the 250 GeV results, this will give a com-plete accounting of the Higgs boson profile. An energyupgrade to 350 GeV begins the use of the ILC as atop quark factory, offering precision measurements of thetop quark mass and electroweak couplings. At the sametime, the ILC will study the reactions e + e − → f f and e + e − → W + W − with high precision. Here also, devia-tions from the SM predictions can indicate new physics.Finally, the ILC will search directly for pair productionof weakly coupled particles with masses up to half thecentre-of-mass energy, without the requirement of spe-cial signatures needed for searches at hadron colliders.Because of its upgrade capability and the unique accessthat e + e − beams give to many important reactions, theILC will continue to be a leading discovery machine inthe world of particle physics for decades.The ILC is mature in its design and ready for con-struction. The technology of the ILC has been advancedthrough a global program coordinated by the Interna-tional Committee for Future Accelerators (ICFA). In themid-1990’s, various technology options to realise a high-energy linear collider were emerging. ICFA asked theLinear Collider Technical Review Committee to developa standardised way to compare these technologies basedon their parameters, such as power consumption and lu-minosity. A second review panel was organised by ICFAin 2002; it concluded that both warm and cold technolo-gies had developed to the point where either could be thebasis for a high energy linear collider. In 2004, the Inter-national Technology Review Panel (ITRP) was chargedby ICFA to recommend an option that could focus theworldwide R&D effort. This panel chose the supercon-ducting radiofrequency technology (SCRF), in a largepart due to its energy efficiency and potential for broaderapplications.Today’s design of the ILC accelerator is the result ofnearly twenty years of R&D that has involved a broad,global community. The heart of the ILC, the SCRF cav-ities, is based on pioneering work of the TESLA Tech-nology Collaboration. Other aspects of the technologyemerged from the R&D carried out for the competinglinear collider projects JLC/GLC and NLC, which werebased on room-temperature accelerating structures. TheILC proposal is supported by extensive R&D and proto-typing. The successful construction and operation of theEuropean XFEL (E-XFEL) at DESY provides confidenceboth in the high reliability of the basic technology andin the reliability of its performance and cost in indus-trial realisation. Other communities acknowledge this;the SCRF technology has also been chosen for new freeelectron laser projects now under construction in the USand China. Some specific optimisations and technologi-cal choices remain. But the ILC is now ready to moveforward to construction.The effort to design and establish the technology forthe linear collider culminated in the publication of theTechnical Design Report (TDR) for the InternationalLinear Collider (ILC) in 2013 [1]. Twenty-four hundred(2400) scientists, from 48 countries and 392 institutesand university groups, signed the TDR. This documentpresented optimised collider and detector designs, andassociated physics analyses based on their expected per-formance. From 2005 to the publication of the TDR,the design of the ILC accelerator was conducted underthe mandate of ICFA as a worldwide international col-laboration, the Global Design Effort (GDE). Since 2013,ICFA has placed the international activities for both theILC and CLIC projects under a single organisation, theLinear Collider Collaboration (LCC).With knowledge of the mass of the Higgs boson, itbecame clear that the linear collider could start its ambi-tious physics program with an initial centre-of-mass en-ergy of 250 GeV at a cost reduced from the TDR. Arevised design of the ILC, the ILC250, was thus pre-sented [2]. This design retains the final-focus and beam-dump capability to extend the centre-of-mass energy toenergies as high as 1 TeV. Advances in the theoreticalunderstanding of the impact of precision measurementsat the ILC250 have justified that the 250 GeV operat-ing point already gives substantial sensitivity to physicsbeyond the SM [3, 4]. The cost estimate for ILC250 issimilar in scale to that of the LHC.In its current form, the ILC250 is a 250 GeV centre-of-mass energy (extendable up to a 1 TeV) linear e + e − collider, based on 1 . . · cm − s − and providean integrated luminosity of 400 fb − in the first four yearsof running. The scenario described in Section III gives acomplete program of 2 ab − of data at 250 GeV over 12years. The electron beam will be polarised to 80 %, andthe baseline plan includes an undulator-based positronsource which will deliver 30 % positron polarisation.The experimental community has developed designsfor two complementary detectors, ILD and SiD. Thesedetectors are described in [5]. They are designed to op- timally address the ILC physics goals, with complemen-tary approaches. One detector is based on TPC tracking(ILD) and one on silicon tracking (SiD). Both employparticle flow calorimetry based on calorimeters with un-precedented fine segmentation. Extensive R&D and pro-totyping gives confidence that the unprecedented levels ofperformance in calorimetry, tracking, and particle iden-tification required to achieve the physics programme canbe realised. The extensive course of prototyping justi-fies our estimates of full-detector performance and cost.The detector R&D program leading to these designs hascontributed a number of advances in detector capabili-ties with applications well beyond the linear collider pro-gram. Similarly to the situation for the collider, somefinal optimizations and technology choices will need tobe completed in the next few years.There is broad interest in Japan to host the interna-tional effort to realise the ILC project. This interest hasbeen growing over many years. Political entities promot-ing the plan to host the ILC in Japan include the Federa-tion of Diet Members for ILC and the Advanced Acceler-ator Association, a consortium of industrial representa-tives that includes most of the large high-tech companiesin Japan. The ILC has been endorsed by the communityof Japanese particle physicists (JAHEP) [6]. Detailedreview in Japan of the many aspects of the project isnearing a conclusion. Since 2013 the MEXT ministry hasbeen examining the ILC project in great detail, includingthe aspect of risk minimisation. This review concludedwhen MEXT’s ILC Advisory Panel released its report [7]on July 4, 2018, summarising the studies of the severalworking groups (WG) that reviewed a broad range ofaspects of the ILC. The most recent studies include aspecific review of the scientific merit and the technicaldesign for the ILC250. The Physics WG scrutinised thescientific merit of the ILC250, leading to their strong andpositive statement on the importance of the ILC250 tomeasure precisely the couplings of the Higgs boson [7].The TDR WG reviewed issues addressed in the TechnicalDesign Report and the ILC250 design, including the costestimate and technical feasibility. Other working groupsof the MEXT review commented on manpower needs,organisational aspects, and the experience of previouslarge projects. The report of the ILC Advisory Panelwas followed by the beginning of deliberations in a com-mittee and technical working group established by theScience Council of Japan (SCJ), the second stage of thereview process. The SCJ released its review on Decem-ber 19, 2018 [8]. The review acknowledges a consensus inthe particle physics community that “the research topicof precise measurement of Higgs couplings is extremelyimportant” but expresses doubts about the cost of theproject, which is well beyond the scale of other propos-als that have come before this committee. The financingof the project will depend on negotiations with interna-tional partners, led by the Japanese government after aclear statement of interest. The Japanese government isnow preparing for this step, which can be followed by amove to the next phase of international negotiations. Anew independent committee (LDP Coordination Councilfor the Realization of ILC), led by high-ranking membersof the Liberal Democratic Party, the majority party inthe Diet, has now convened to encourage the nationalgovernment along this path.Given a positive signal by the Japanese government,the ILC could move forward rapidly. The potential time-line would have an initial period of about 4 years to ob-tain international agreements, prepare for the construc-tion, and form the international laboratory and its gov-ernance structure. The construction phase would thenneed 9 years.It is an important aspect of the discussions of the ILCin Japan that the ILC has been organized from the begin-ning as a global project that will foster exchange betweenJapan and other nations. Thus, the scientific interest andpolitical engagement of partner countries is of major im-portance for the Japanese authorities.The purpose of this report is to set out in detail thecurrent status of the ILC project, expanding on a recentpaper prepared as input to the Update of the EuropeanStrategy for Particle Physics [9]. We discuss the physicsreach of the ILC, the technological maturity of the ac-celerator, detector, and software/computing designs, andthe further steps needed to concretely realise the project.Section 2 describes the accelerator design and technol-ogy, reviewing both current status of SCRF developmentand the general layout of the machine. This section alsopresents luminosity and energy upgrade options, as wellas civil engineering plans, including site specific details,and cost and schedule estimates. Section 3 presents thecurrent thinking about the operations of the ILC, withestimates of the plan and schedule for the collection ofintegrated luminosity. Section 4 gives an overview of thephysics case for the ILC as a 250 GeV collider. This in-cludes a more detailed discussion of the significance of theHiggs boson as a tool for searching for physics beyond theSM, the qualitative comparison of the ILC to the LHCas a facility for precision Higgs studies, and the theoret-ical approach for extracting Higgs boson couplings from e + e − data. This section also discusses the physics oppor-tunities of searches for exotic Higgs decays and studiesof other processes of interest including SM fermion pair-production and searches for new particle pair production.Section 5 described the additional opportunities that theenergy extension to 500 GeV will make available.Section 6 provides detailed descriptions of the ILC de-tector designs that have been developed by the commu-nity, through detector R&D and prototyping, and usedas detector models to show the simulated performance onthe various physics channels. Section 7 summarises thecomputing needs of the ILC program, including software.These two sections provide the basis for a discussion ofthe experimental measurements of reactions crucial tothe ILC program. All of the projections of experimen-tal uncertainties given in this paper are based on full-simulation studies using the model detectors described in Sec. 6, with capabilities justified by extensive R&Dprograms.Building on this discussion, Sec. 8 gives a descriptionof physics simulations involving Higgs boson reactions.Section 9 describes physics simulations carried out for thereactions e + e − → W + W − and e + e − → f f . Section 10discusses simulations of measurements of top quark prop-erties at the energy-upgraded ILC. These studies lead toconcrete quantitative estimates for the expected uncer-tainties in Higgs boson coupling determinations. Basedon the results of these studies, we present in Sec. 11 whatwe feel are conservative estimates for the precision thatthe ILC will attain in a highly model-independent analsysfor the determination of the Higgs boson width and abso-lutely normalized couplings. We compare these estimatesto those presented in the CDRs for other e + e − Higgs fac-tories and those expected from the high-luminosity phaseof the LHC.Section 12 describes the capability of the ILC for di-rect searches for pair-production of new particles, cover-ing a number of scenarios that are difficult for the LHCbut which can be investigated in detail at e + e − colliders.Section 13 gives our conclusions.
2. ILC MACHINE DESIGN
The International Linear Collider (ILC) is a 250 GeV(extendable up to 1 TeV) linear e + e − collider, based on1 . . · cm − s − and provide an integrated luminosity of400 fb − in the first four years of running. The elec-tron beam will be polarised to 80 %, and positrons with30 % polarization will be provided if the undulator basedpositron source concept is employed.Its parameters have been set by physics requirementsfirst outlined in 2003, updated in 2006, and thoroughlydiscussed over many years with the physics user com-munity. After the discovery of the Higgs boson it wasdecided that an initial energy of 250 GeV provides theopportunity for a precision Standard Model and Higgsphysics programme at a reduced initial cost [2]. Some rel-evant parameters are given in Tab. I. This design evolvedfrom two decades of R&D, described in Sec. 1, an inter-national effort coordinated first by the GDE under ICFAmandate and since 2013 by the LCC.The fundamental goal of the design of the ILC accel-erator is a high energy-efficiency. The ILC design limitsthe overall power consumption of the accelerator complexduring operation to 129 MW at 250 GeV and 300 MW at1 TeV, which is comparable to the power consumption ofCERN. This is achieved by the use of SCRF technologyfor the main accelerator, which offers a high RF-to-beamefficiency through the use of superconducting cavities,operating at 1 . . / m this technology offers high overall efficiency Quantity Symbol Unit Initial L Upgrade TDR UpgradesCentre of mass energy √ s GeV 250 250 250 500 1000Luminosity L cm − s − .
35 2 . .
82 1 . / . . e − ( e + ) P − ( P + ) 80 %(30 %) 80 %(30 %) 80 %(30 %) 80 %(30 %) 80 %(20 %)Repetition frequency f rep Hz 5 5 5 5 4Bunches per pulse n bunch / N e . t b ns 554 366 554 554 /
366 366Beam current in pulse I pulse mA 5 . . . . . t pulse µ s 727 961 727 727 /
961 897Average beam power P ave MW 5 . . . . /
21 27 . γ(cid:15) x µ m 5 5 10 10 10Norm. vert. emitt. at IP γ(cid:15) y nm 35 35 35 35 30RMS hor. beam size at IP σ ∗ x nm 516 516 729 474 335RMS vert. beam size at IP σ ∗ y nm 7 . . . . . L . / L
73 % 73 % 87 . . . δ BS . . .
97 % 4 . . P site MW 129 122 163 300Site length L site km 20 . . . · cm − s − [10]. and reasonable investment costs, even considering thecryogenic infrastructure needed for the operation at 2 K.The underlying TESLA technology is mature, with abroad industrial base throughout the world, and is inuse at a number of free electron laser facilities that arein operation (E-XFEL at DESY, Hamburg), under con-struction (LCLS-II at SLAC, Stanford) or in preparation(SCLF in Shanghai) in the three regions Asia, Americas,and Europe that contribute to the ILC project. In prepa-ration for the ILC, Japan and the U.S. have founded acollaboration for further cost optimisation of the TESLAtechnology. In recent years, new surface treatment tech-nologies utilising nitrogen during the cavity preparationprocess, such as the so-called nitrogen infusion technique,have been developed at Fermilab, with the prospect ofachieving higher gradients and lower loss rates with aless expensive surface preparation scheme than assumedin the TDR (see Sec. 2.2.1).When the Higgs boson was discovered in 2012, theJapan Association of High Energy Physicists (JAHEP)made a proposal to host the ILC in Japan [11, 12]. Sub-sequently, the Japanese ILC Strategy Council conducteda survey of possible sites for the ILC in Japan, lookingfor suitable geological conditions for a tunnel up to 50 kmin length (as required for a 1 TeV machine), and the pos-sibility to establish a laboratory where several thousandinternational scientists can work and live. As a result,the candidate site in the Kitakami region in northernJapan, close to the larger cities of Sendai and Morioka,was found to be the best option. The site offers a large,uniform granite formation with no currently active faultsand a geology that is well suited for tunnelling. Even inthe great Tohoku earthquake in 2011, underground in-stallations in this rock formation were essentially unaf-fected [13], which underlines the suitability of this can- didate site.This section starts with a short overview over thechanges of the ILC design between the publication of theTDR in 2013 and today, followed by a description of theSCRF technology, and an description of the overall ac-celerator design and its subsystems. Thereafter, possibleupgrade options are laid out, the Japanese candidate sitein the Kitakami region is presented, and costs and sched-ule of the accelerator construction project are shown. Soon after the discovery of the Higgs boson, the Tech-nical Design Report (TDR) for the ILC accelerator waspublished in 2013 [14, 15] after 8 years of work by theGlobal Design Effort (GDE). The TDR design was basedon the requirements set forth by the ICFA mandated pa-rameters committee [16]: • a centre-of-mass energy of up to 500 GeV, • tunability of the centre-of-mass energy between √ s = 200 GeV and 500 GeV, • a luminosity sufficient to collect 500 fb − withinfour years of operation, taking into account a three-year a ramp up. This corresponds to a final lumi-nosity of 250 fb − per year and an instantaneousluminosity of L = 2 · cm − s − , • an electron polarisation of at least 80 %, • the option for a later upgrade to energies up to1 TeV.The accelerator design presented in the TDR met theserequirements (see Tab. I), at an estimated constructioncost of 7 ,
982 MILCU for a Japanese site, plus 22 . centralregion ~20.5 km ~7.5 km ~7.4 km FIG. 1: Schematic layout of the ILC in the 250 GeV staged configuration. (million hours) of labour in participating institutes [15,Sec. 15.8.4]. Costs were expressed in ILC Currency UnitsILCU, where 1 ILCU corresponds to 1 US$ at 2012 prices.In the wake of the Higgs discovery, and the proposalby the Japan Association of High Energy Physicists (JA-HEP) to host the ILC in Japan[11] with its recommen-dation to start with a 250 GeV machine [12], plans weremade for a less expensive machine configuration witha centre–of–mass energy of √ s = 250 GeV, around themaximum of the Zh production cross section, half theTDR value. Various options were studied in the TDR [15,Sect. 12.5] and later [17]. This resulted in a revised pro-posal [2] for an accelerator with an energy of 250 GeVand a luminosity of L = 1 . · cm − s − , capableof delivering about 200 fb − per year, or 400 fb − withinthe first four years of operation, taking into account theramp-up.Several other changes of the accelerator design havebeen approved by the ILC Change Management Boardsince 2013, in particular: • The free space between the interaction point andthe edge of the final focus quadrupoles ( L ∗ ) wasunified between the ILD and SiD detectors [18],facilitating a machine layout with the best possibleluminosity for both detectors. • A vertical access shaft to the experimental cav-ern was foreseen [19], allowing a CMS-style assem-bly concept for the detectors, where large detectorparts are built in an above-ground hall while theunderground cavern is still being prepared. • The shield wall thickness in the Main Linac tunnelwas reduced from 3 . . • Power ratings for the main beam dumps, and inter-mediate beam dumps for beam aborts and machinetuning, were reduced to save costs [21]. • A revision of the expected horizontal beam emit-tance at the interaction point at 125 GeV beam en-ergy, based on improved performance expectationsfor the damping rings and a more thorough scrutinyof beam transport effects at lower beam energies,lead to an increase of the luminosity expectationfrom 0 .
82 to 1 . · cm − s − [22]. • The active length of the positron source undulatorhas been increased from 147 to 231 m to providesufficient intensity at 125 GeV beam energy [23].These changes contributed to an overall cost reduction,risk mitigation, and improved performance expectation.Several possibilities were evaluated for the length of theinitial tunnel. Options that include building tunnels withthe length required for a machine with √ s = 350 GeV or500 GeV, were considered. In these scenarios, an energyupgrade would require the installation of additional cry-omodules (with RF and cryogenic supplies), but littleor no civil engineering activities. In order to be as costeffective as possible, the final proposal (see Figure 1), en-dorsed by ICFA [24], does not include these empty tunneloptions.While the length of the main linac tunnel was reduced,the beam delivery system and the main dumps are stilldesigned to allow for an energy upgrade up to √ s =1 TeV. FIG. 2: A 1 . The heart of the ILC accelerator consists of the two su-perconducting Main Linacs that accelerate both beamsfrom 5 to 125 GeV. These linacs are based on the TESLAtechnology: beams are accelerated in 1 . FIG. 3: An ILC type cryomodule. c (cid:13)
Rey.Hori/KEK.
The single most important parameter for the cost andperformance of the ILC is the accelerating gradient g .The TDR baseline value is an average gradient g =31 . / m for beam operation, with a ±
20 % gradient spread between individual cavities. Recent progress inR&D for high gradient cavities raises the hope to in-crease the gradient by 10 % to g = 35 MV / m, whichwould reduce the total cost of the 250 GeV acceleratorby about 6 %. To achieve the desired gradient in beamoperation, the gradient achieved in the low-power ver-tical test (mass production acceptance test) is specified10 % higher to allow for operational gradient overhead forlow-level RF (LLRF) controls, as well as some degrada-tion during cryomodule assembly (few MV / m). Figure 4shows how the achievable gradients have evolved over thepast 50 years [31]. a. Gradient impact on costs: To the extent that thecost of cavities, cryomodules and tunnel infrastructure isindependent of the achievable gradient, the investmentcost per GeV of beam energy is inversely proportionalto the average gradient achieved. This is the reason forthe enormous cost saving potential from higher gradients.This effect is partially offset by two factors: the energystored in the electromagnetic field of the cavity, and thedynamic heat load to the cavity from the electromagneticfield. These grow quadratically with the gradient for onecavity, and therefore linearly for a given beam energy.The electromagnetic energy stored in the cavity must bereplenished by the RF source during the filling time thatprecedes the time when the RF is used to accelerate thebeam passing through the cavity; this energy is lost aftereach pulse and thus reduces the overall efficiency and re-quires more or more powerful modulators and klystrons.The overall cryogenic load is dominated by the dynamicheat load from the cavities, and thus operation at highergradient requires larger cryogenic capacity. Cost mod-els that parametrise these effects indicate that the mini-mum of the investment cost per GeV beam energy lies at50 or more GeV, depending on the relative costs of tun-nel, SCRF infrastructure and cryo plants, and dependingon the achievable Q [32]. Thus, the optimal gradientis significantly higher than the value of approximately35 MV / m that is currently realistic; this emphasises therelevance of achieving higher gradients.It should be noted that in contrast to the initial in-vestment, the operating costs rise when the gradient isincreased, and this must be factored into the cost model. b. Gradient limitations: Fundamentally, the achiev-able gradient of a SC cavity is limited when the mag-netic field at the cavity walls surpasses the critical field H crit , RF of the superconductor. This gradient dependson the material, operating temperature, and the cavitygeometry. For the TESLA type cavities employed at theILC, this limit is about 48 MV / m at 2 K. The best E-XFEL production cavity reached 44 . / m (Fig. 5).The record for single cell cavities operating at 1 . / m [33].Niobium is a type-II superconductor, and so it has twodistinct superconducting phases, the Meissner state, withcomplete magnetic flux expulsion, which exists up to afield strength H c1 ≈
180 mT /µ ( µ = 4 π − T m / A be-ing the vacuum permeability), and a mixed state in which
L-band SRF Linear Accelerator Technology
Impact to Nuclear, Elementary Particle, and Photon Sciences and Medical Applications E a cc [ M V / m ] Year
CW SRF Linacs:SCA: Stanford Superconducting AcceleratorMUSL: llinois Microtron Using a Supersoducting LinacCEBAF: Continuous Electron Beam Accelerator FacilityJLAB FEL: Jefferson Lab Free Electron LaserELBE: HZDR Electron Linear accelerator with high Brillance and Low EmittanceALICE: STFC Accelerators and Lasers In Combined ExperimentsARIEL: TRIUMF Advanced Rare IsotopE LaboratoryLCLS-II: Linac Coherence Light Source extensionSHINE: Shanghai High Brightness Photon Facility Pulsed SRF Linacs:FAST: Fermilab Accelerator Science and Technology FacilitySTF: KEK Superconducting RF Test FacilityE-XFEL: European X-Ray Free Electron LaserILC: International Linear Collider
SCA physics and FEL run (300 MeV)
CEBAF Goal TESLA Goal CEBAF 12 GeV Upgrade Goal C EBA F M odu l e TTF M odu l e LCLS-II photon science
LCLS-II Goal
MUSL-II nuclear physics run (80 MeV)MUSL-I SCA FEL run (65 MeV) for physics, chemistry, biology, medicineCEBAF 4 - 5.7 GeV physics run
Today
CEBAF 12 GeV upgrade2X 1.1 GeV linac
CEBAF 12 GeV nuclear physics
TTF SASE FEL run E-XFEL construction17.5 GeV linac
E-XFEL photon scienceILC Goal PX F E L1 M odu l e D ESY X M - M odu l e F N A L C M M odu l e ILC construction2X 125 GeV linacILC 1 TeV upgradeHigh Gradient R&DRLGENG28DEC2018
Single-Cell Cavity H EP L M odu l e Multi-Cell Cavity
LCLS-IIconstruction4 GeV linac
KEK C M - + C M - M odu l e STF ILC 1TeV R&D Goal
SHINE construction 8 GeV linac
SHINEphotonscience
FASTJLAB FEL ELBE ALICE
CEBAF 6 GeV physics run C EBA F M odu l e R e - w o r k ARIELconstruction ARIELnuclear medicineproduction run
FIG. 4: Development of the gradient of SRF cavities since 1970 [31, updated]. flux vortices penetrate the material, up to a higher fieldstrength H c1 , at which superconductivity breaks downcompletely. In time-dependent fields, the penetratingvortices move due to the changing fields and thus dis-sipate energy, causing a thermal breakdown. However,for RF fields, the Meissner state may persist metastablyup to the superheating field strength H sh ≈
240 mT /µ ,which is expected to be the critical RF field criticalfield H crit , RF [34]. Experimentally, niobium RF cavi-ties have been operated at field strengths as high as H = 206 mT /µ [33], and the best E-XFEL productioncavities reach about 190 mT. Recently, even 210 mT hasbeen achieved at FNAL [35]. In recent years, theoreticalunderstanding of the nature of this metastable state andthe mechanisms at the surface that prevent flux pene-tration has significantly improved [36, 37]. It appearsthat a thin layer of “dirty” niobium, i.e. , with intersti-tial impurities, on top of a clean bulk with good thermalconductivity, is favourable for high field operation.The gradient at which a SC cavity can be operated inpractice is limited by three factors in addition to thosejust listed [34]: • the thermal breakdown of superconductivity, whenlocal power dissipation causes a local quench of thesuperconductor, • the decrease of the quality factor Q at high gradi-ents that leads to increased power dissipation, • the onset of field emission that causes the break- down of the field in the cavity.The onset of these adverse effects is mostly caused bymicro-metre sized surface defects of various kinds. Pro-ducing a sufficiently defect-free surface in an economicway is thus the central challenge in cavity production.More than 20 years of industrial production of TESLAtype cavities have resulted in a good understanding whichproduction steps and quality controls are necessary toproduce cavities with high-quality, nearly defect-free sur-faces that are capable of achieving the desired high fieldstrengths at a reasonable production yield. c. Results from E-XFEL cavity production: Theproduction and testing of 831 cavities for the E-XFEL [38, 39] provides the biggest sample of cavity pro-duction data so far. Cavities were acquired from twodifferent vendors, RI and EZ. Vendor RI employed a pro-duction process with a final surface treatment closelyfollowing the ILC specifications, including a final elec-tropolishing (EP) step, while the second vendor EZ usedbuffered chemical polishing (BCP). The E-XFEL specifi-cations asked for a usable gradient of 23 . / m with a Q ≥ · for operation in the cryomodule; with a 10 %margin this corresponds to a target value of 26 MV / m forthe performance in the vertical test stand for single cavi-ties. Figure 5 shows the Q data versus accelerating gra-dient of the best cavities received, with several cavitiesreaching more than 40 MV / m, significantly beyond theILC goal, already with Q values that approach the tar-get value 1 . · that is the goal of future high-gradient0 Goal ILC:E usable ≥ ≥ ·10 Text
Text
Text
R&D Goal ILC:E usable ≥
35 MV/mQ ≥ ·10 FIG. 5: Examples of the Q ( E acc ) curves of some of thebest cavities, either treated at RI using “EP final”, or at EZusing “BCP flash.” [38, Fig. 19]. Vendor “RI” employs aproduction process that closely follows the ILCspecifications, with a final electropolishing step. The ILCgradient / Q goals are overlaid. R&D.
FIG. 6: Distribution and yield of the “as received”maximum gradient of cavities produced for the E-XFEL,separated by vendor [39, Fig. 33]. Vendor RI employs aproduction process that closely follows the ILCspecifications, with a final electro polishing step.
E-XFEL production data, in particular from vendorRI, provide excellent statistics for the cavity performanceas received from the vendors, as shown in Fig. 6. Forvendor RI, the yield for cavities with a maximum gradientabove 28 MV / m is 85 %, with an average of 35 . / mfor the cavities that pass the cut.Since the E-XFEL performance goal was substantiallylower than the ILC specifications, cavities with gradi-ent below 28 MV / m, which would not meet ILC speci-fications, were not generally re-treated for higher gradi-ents, limiting our knowledge of the effectiveness of re-treatment for large gradients. Still, with some extrapo-lation it is possible to extract yield numbers applicable to the ILC specifications [40].The E-XFEL data indicate that after re-treating cav-ities with gradients outside the ILC specification of35 MV / m ±
20 %, i.e. , below 28 MV / m, a yield of 94 %for a maximum gradient above 28 MV / m can be achieved,with an average value of 35 MV / m, meeting the ILC spec-ification. Taking into account limitations from Q andthe onset of field emission, the usable gradient is lower.This gives a 82 (91) % yield and an average usable gra-dient of 33 . / m after up to one (two) re-treatments.The re-treatment and testing rate is significantly higherthan assumed in the TDR, but the E-XFEL experienceshows that re-treatment can mostly be limited to a sim-ple high-pressure rinse (HPR) rather than an expensiveelectropolishing step.Overall, the E-XFEL cavity production data provethat it is possible to mass-produce cavities meeting theILC specifications as laid out in the TDR with the re-quired performance and yield. FIG. 7: Effect of successive cavity treatments on a singlecavity: 800 ◦ C bake for five days (black, lowest curve),followed by 48 hours baking at 120 ◦ C (red, middle curve).A third heat treatment including nitrogen infusion (green,top curve) significantly raises the breakdown gradient andthe quality factor of the cavity [41, Fig. 5]. d. High-gradient R&D – nitrogen infusion:
In re-cent years, new techniques have emerged that seem toindicate that higher gradients combined with higher qual-ity factors are attainable in bulk niobium cavities.In the early 2010s, nitrogen doping was developed asa method to substantially increase Q by adding nitro-gen during the 800 ◦ C baking, which leads to interstitialnitrogen close to the niobium surface [42]. This tech-nique has been employed successfully in the productionof the cavities for LCLS-II, with an average Q of 3 . · achieved in a prototype cryomodule [43]. However, nitro-gen doping reduces the critical RF field of the materialand thus limits the achievable gradients to values below130 MV / m, rendering doped material useless for high gra-dient applications.By contrast, in nitrogen infusion the nitrogen is addedduring the low temperature baking at 120 ◦ C. Exper-imental results seem to indicate that nitrogen infusionmay offer a combination of three advantages: • Reaching higher accelerating gradients, • higher Q values, resulting in a reduced cryogenicload, • a simplified and less expensive production processthat does away with the final electropolishing step.Figure 7 [41, Fig. 19] shows how the addition of nitro-gen during the final 48 h long 120 ◦ C bake of a one–cellcavity drastically improves the cavity quality factor aswell as the maximum gradient, which comes close to thebest E-XFEL cavity results, but at higher Q .Up to now, it has been difficult to reproduce theseexciting results in other laboratories. Success has beenreported by groups at JLAB [44], and Cornell [45], butKEK has reported mixed results [46], and DESY has sofar not been able to reproduce these results [47]. Thesedifficulties seem to indicate that the recipe for a suc-cessful application of nitrogen infusion is not yet fullyunderstood, and that further research and developmentwill be necessary before this process can be transferredto industry.Nevertheless, the infusion results have triggered a re-newed interest in the research on highest gradients in nio-bium cavities, with a host of new experimental results,increased activity to achieve a more thorough theoreticalunderstanding [36, 37], and application of state-of-the-artanalytical methods such as muon spin rotation (muSR)[48]. Recently, a record gradient for TESLA shape cav-ities of 49 MV / m was reported [35] with a low tempera-ture treatment at 75 ◦ C after 120 ◦ C baking without ni-trogen. All these results provide reason for optimism thatan improved understanding of the mechanisms that sta-bilise superconductivity in the presence of high fields willresult in improved performance of industrially producedcavities for the ILC. e. High-gradient R&D – alternative cavity shapes:
Fundamentally, the achievable gradient in a niobium cav-ity is limited by the maximum magnetic field at the cavitysurface, not the electrical field strengths. The ratio be-tween peak surface field B pk and gradient g depends onthe cavity geometry and is B pk /g = 4 .
26 mT / (MV / m)for TESLA type cavities. A number of alternative cav-ity shapes have been investigated with lower ratios [49],resulting in single cells gradients up to 59 MV / m [33].The reduced magnetic field, however, has to be balancedwith other factors that favour the TESLA cavity shape,namely: a reasonable peak electrical field to limit the riskof field emission, sufficient iris width and cell-to–cell RFcoupling, and a mechanical shape that can be efficientlyfabricated. Recently, new five-cell cavities with a new “low surfacefield” (LSF) shape [50] have been produced at JLAB andhave achieved gradient of up to 50 MV / m in three of thefive cells, which is a new record for multi-cell cavities [51].The LSF shape aims to achieve a good compromise be-tween the goal of a low magnetic field and the other crite-ria, and demonstrates that further improvements in gra-dient may be realised in the future. Additional strategies for cost reduction and improvedcavity performance are also being investigated. a. Low
RRR material:
The niobium raw materialand preparation of sheets are a significant cost driver;R&D is underway to re-evaluate the stringent limits onimpurities, especially of tantalum, and the demand fora high residual resistivity ratio
RRR > , to reducethe raw material cost. The electrical conductivity andheat transport by electrons are proportional. This im-plies that large RRR values, indicative of low impuritycontent, make the cavities also less susceptible to thermalbreakdown from surface defects. However, when defectsizes can be successfully controlled to the extent neces-sary to achieve gradients above 35 MV / m routinely, theinfluence of heat conductivity and RRR may be dimin-ished, permitting the use of lower
RRR material [52]. b. Ingot and large-grain niobium:
Together with di-rect slicing of discs from large niobium ingots, withoutrolling, forging and grinding or polishing steps, the costfor niobium sheets has the potential to be reduced by50 % [2, 53]. Without the mechanical deformation duringrolling and forging, the grains from the initial crystalli-sation stay large, which makes later production steps,in particular deep–drawing of half cells, more challeng-ing. Nevertheless, if these challenges are overcome, testswith large–grain and ingot niobium show promising re-sults [54, 55].
The choice of operating frequency is a balance betweenthe higher cost of larger, lower-frequency cavities andthe increased cost at higher frequency associated withthe lower sustainable gradient from the increased surfaceresistivity. The optimum frequency is in the region of1 . . RRR is the ratio of the material’s room temperature resistivityto the normal conducting resistivity close to 0 K; heat conduc-tivity from electrons is proportial to
RRR . RRR is reduced byimpurities, in particular interstitial ones from hydrogen, nitrogenand oxygen. The superconducting accelerating cavities for the ILCare nine-cell structures made out of high-purity niobium(Fig. 2), with an overall length of 1 .
25 m. Cavity pro-duction starts from niobium ingots which are forged androlled into 2 . ◦ C and 120 ◦ C, and electropolishing or bufferedchemical polishing. The recipe for the surface prepara-tion has been developed over a long time. Still, it remainssubject to optimisation, since it is a major cost driver forthe cavity production and largely determines the overallperformance and yield of the cavities. In particular theelectropolishing steps are complicated and costly, as theyrequire complex infrastructure and highly toxic chemi-cals. One advantage of nitrogen infusion (see Sec. 2.2.1)is that the final electropolishing step is omitted.Careful quality control during the production processis of high importance. At the E-XFEL, several qual-ity controls were conducted by the manufacturer duringproduction, with nonconformities reported to the insti-tute responsible for the procurement, where a decisionwas made whether to accept or reject a part [38]. Withthis “build to print” approach, in which the manufac-turer guarantees that a precise production process will befollowed but does not guarantee a specific performance,procurement costs are reduced, because the manufacturerdoes not carry, and does not charge for, the performancerisk.Upon reception from the manufacturer, cavities aretested in a vertical cryostat (“vertical test”), where Q is measured as a function of the gradient. Cavities thatfall below the specified gradient goal are re-treated byan additional (expensive) electropolishing step or a com-paratively simple high-pressure rinse. After retreatment,the vertical test is repeated.Re-treatment and tests constitute a major cost driverin cavity production. For the ILC TDR, it was assumed that 25 % of the cavities would fall below the 28 MV / mgradient threshold and undergo re-treatment and a sec-ond vertical test. E-XFEL data from the vendor “RI”that followed the ILC production recipe indicate that15 % to 37 % of the cavities fall below 28 MV / m, depend-ing on whether the maximum or the “usable” achievedgradient is considered [40]. However, E-XFEL experiencealso shows that, in most of the cases, a high-pressure rinseis sufficient as re-treatment to remove surface defects,which is a cost saving compared to the electropolishingassumed in the TDR.After successful testing, prior to installation in the cry-omodule, cavities are equipped with a magnetic shieldand the frequency tuner, which exerts mechanical forceon the cavity to adjust the resonant frequency to the fre-quency of the external RF field [15, Sect. 3.3]. The power coupler transfers the radio frequency (RF)power from the waveguide system to the cavity. In theILC, a coupler with a variable coupling is employed; thisis realised using a movable antenna. Another role of thecoupler is to separate the cavity vacuum from the atmo-spheric pressure in the waveguide, and to insulate thecavity at 2 K from the surrounding room temperature.Thus, the coupler has to fulfill a number of demanding re-quirements: transmission of high RF power with minimallosses and no sparking, vacuum tightness and robustnessagainst window breaking, and minimal heat conductivity.As a consequence, the coupler design is highly complex,with a large number of components and several criticalhigh-tech manufacturing steps.The baseline coupler design was originally developedin the 1990s for the TESLA Test Facility (TTF, nowFLASH) at DESY, and has since been modified by acollaboration of LAL and DESY for use in the E-XFEL.About 840 of these couplers (depicted in Fig. 8) were fab-ricated by three different companies for the E-XFEL [56],where 800 are now in operation. A lot of experience hasbeen gained from this production [57]. waveguide to coax transitionroom temperature window warm vacuum pumping portQext tuning rod room temperature isolating vacuum flangecold windowwarm coax ∅ Ω
70K pointcold coax ∅ Ω FIG. 8: An E-XFEL type coupler. To facilitate transportation, installation and operation,8 or 9 cavities are integrated into a 12 . −
80 K temperature.
FIG. 9: View of installed cryomodules in the tunnel of theE-XFEL [58].
Nine of these cryomodules are connected in the tunnelto form a cryostring with a common liquid helium sup-ply. RF for one such string is provided by two klystrons.No separate helium transfer line is necessary, as all he-lium transport lines are integrated within the modules.A quadrupole / beam position monitor / corrector mag-net unit is mounted instead of the 9th cavity in everythird module. Figure 9 shows installed cryomodules inthe tunnel of the E-XFEL [58].Cryomodule assembly requires a dedicated facility withlarge clean rooms, especially trained, experienced person-nel, and thorough quality control [59]. The cryomodulesare certified for liquid helium pressure of up to 2 bar.Thus they must conform to the applicable pressure vesselcodes, which brings with it very stringent documentationrequirements for all pressure bearing parts [60].For the E-XFEL project, 103 cryomodules were assem-bled in a facility built and operated by CEA [59, 61] andindustrial partners, demonstrating the successful indus-trialization of the assembly process, with a final through-put of one cryomodule every four working days. This pro-duction rate is close to the rate envisaged for a possibleEuropean contribution of 300 cryomodules to a 250 GeVILC in Japan.While the design gradient for E-XFEL acceleratormodules of 23 . / m is significantly lower than the aimof 31 . −
35 MV / m for the ILC, a number of cryomoduleshave been built around the world that come close or reachthe ILC TDR specification of 31 . / m: An E-XFELprototype module at DESY reached 30 MV / m [62], Fer-milab has demonstrated cryomodule operation at the ILCspecification of 31 . / m [63], and KEK has reported stable pulsed operation of a cryomodule at 36 MV / m [64]. FIG. 10: Average of the operating (blue) and maximum(green) gradient for cavities in each E-XFELserial-production cryomodule. The specification of23 . / m is marked by a red line [65]. Modules 98 and 99were assembled from the lowest-performing cavities. Figure 10 shows the average cavity gradients per cry-omodule for the E-XFEL serial-production cryomod-ules [65]. In the tests, the gradients were limited ad-ministratively to 31 MV / m; the true maxima might behigher. For almost all of the modules, the cavity gradi-ents are significantly above the E-XFEL specification of23 . / m. In order to allow various designs of sub-components fromdifferent countries and vendors to work together in thesame cryomodule, a set of interface definitions has beeninternationally agreed upon. This “plug-compatible” de-sign ensures that components are interchangeable be-tween modules from different regions and thus reducesthe cost risk. Corresponding interface definitions existfor the cavity, the fundamental-mode power coupler, themechanical tuner and the helium tank. The “S1Global”project [66] has successfully built a single cryomodulefrom several cavities equipped with different couplers andtuners, demonstrating the viability of this concept.
The high-level radio-frequency (HLRF) system providesthe RF power that drives the accelerating cavities. Thesystem comprises modulators, pulsed klystrons, and awaveguide power distribution system. a. Modulators:
The modulators provide the short,high-power electrical pulses required by the pulsedklystrons from a continuous supply of electricity. TheILC design foresees the use of novel, solid state Marx4modulators. These modulators are based on a solid-state switched capacitor network, where capacitors arecharged in parallel over the long time between pulses,and discharged in series during the short pulse dura-tion, transforming continuous low-current, low voltageelectricity into short high-power pulses of the requiredhigh voltage of 120 kV at a current of 140 A, over 1 .
65 ms.Such Marx modulators have been developed at SLAC [67]and successfully tested at KEK [68]. However, long-termdata about the required large mean time between failures(MTFB) are not yet available. b. Klystrons:
The RF power to drive the accelerat-ing cavities is provided by 10 MW L-band multi-beamklystrons. Devices meeting the ILC specifications wereinitially developed for the TESLA project, and laterfor the E-XFEL. They are now commercially availablefrom two vendors (Thales and Toshiba), both of whichprovided klystrons for the E-XFEL. The ILC specifica-tions ask for a 65 % efficiency (drive beam to output RFpower), which are met by the existing devices.Recently, the High Efficiency International KlystronActivity (HEIKA) collaboration [69, 70] has been formedthat investigates novel techniques for high–efficiencyklystrons. Taking advantage of modern beam dynamictools, methods such as the Bunching, Alignment andCollecting (BAC) method [71] and the Core OscillationMethod (COM) [72] (Fig. 11) have been developed thatpromise increased efficiencies up to 90 % [73]. One advan-tage of these methods is that it is possible to increase theefficiency of existing klystrons by equipping them with anew electron optics, as was demonstrated retrofitting anexisting tube from VDBT, Moscow. This increased theoutput power by almost 50 % and its efficiency from 42 %to 66 % [74].To operate the ILC at an increased gradient of35 MV / m would require that the maximum klystron out-put power is increased from 10 to 11 MW. It is assumedthat this will be possible by applying the results fromthis R&D effort to high-efficiency klystrons. FIG. 11: Electron phase profile of an 800 MHz klystronemploying the Core Oscillation Method (COM) [72]. c. Local Power–Distribution System (LPDS):
In thebaseline design, a single RF station with one modula-tor and klystron supplies RF to 39 cavities, which cor-responds to 4 . ±
20 % to allow for the specified spread in maxi-mum gradient. The LPDS design therefore contains re-motely controlled, motor-driven Variable Power Dividers(VPD), phase shifters, and H–hybrids that can distributethe power with the required flexibility. This design al-lows one to optimise the power distribution during oper-ation, based on the cavity performance in the installedcryomodule, and thus to get the optimum performanceout of the system. It does not require a measurementof the individual cavity gradients after the module as-sembly, and is thus compatible with the ILC productionscheme, where only a fraction of the cryomodules aretested. This is a notable difference from the scheme em-ployed at the E-XFEL, where 100 % of the modules weretested, and the the power distribution for each modulewas tailored to the measured cavity gradients, saving in-vestment costs for the LPDS but making the system lessflexible.
The operation of the large number of superconductingcryomodules for the main linacs and the linacs associ-ated with the sources requires a large–scale supply ofliquid helium. The cyomodules operate at 2 K and arecooled with superfluid helium, which at 2 K has a vapourpressure of about 32 mbar.The accelerator is supplied with liquid helium by sev-eral cryogenic plants [15, Sec. 3.5] of a size similar tothose in operation at CERN for the LHC, at Fermilab,and DESY, with a cooling capacity equivalent to about19 kW at 4 . . Due to the construction of the E-XFEL, the industrialbasis for the key SCRF components is broad and mature,in particular in Europe. Europe has a leading supplierfor raw material. In all three regions (Europe, Amer-ica, Asia), several vendors for cavities have been quali-5fied for ILC type cavities, and provided cost estimatesin the past. Two leading cavity vendors are Europeancompanies that have profited from large scale produc-tion of cavities for E-XFEL; both have won contracts forLCLS-II as a consequence. RF couplers have also beensuccessfully produced by European and American ven-dors for the E-XFEL and LCLS-II projects.ILC/TESLA type cryomodules have been built in labo-ratories around the world (DESY, CEA in Europe, FNALand JLAB in America, KEK in Asia). Series productionhas been established in America at Fermilab and JLABfor LCLS-II. The largest series production was conductedby CEA in France, again for the E-XFEL, with the as-sembly of 103 cryomodules in total by an industrial part-ner under the supervision of CEA personnel, with a finalthroughput of one cryomodule produced every four work-ing days.ILC type, pulsed 10 MW klystrons are commerciallyavailable from two vendors in Japan and Europe.For E-XFEL, China has been a supplier for niobiumraw material and cryomodule cold masses (the cryostatwith internal insulation and tubing). For the plannedSCLF project in Shanghai, China has started to developcavity and cryomodule production capabilities, whichwill further broaden the worldwide production capabil-ities for SCRF components. This reduces the risk thatprices are pushed up by a monopoly of manufacturers fora large scale order of components as required for the ILC.Overall, European industry is well prepared to producethe high-tech, high-value SCRF components needed forthe ILC, which would likely constitute the largest frac-tion of any European in-kind contribution (IKC) to theILC, at very competitive prices. Thus, expenditure forthe European IKC will likely stay in Europe, with an ex-cellent chance to stay within the price range assumed inthe value estimate. Moreover, European companies arewell positioned to win additional contracts from otherregions, increasing the economic benefit for Europe froman ILC project.
The electron and positron sources are designed to pro-duce 5 GeV beam pulses with a bunch charge that is 50 %higher than the design bunch charge of 3 . · e),in order to have sufficient reserve to compensate any un-foreseen inefficiencies in the beam transport. In the base-line design, both sources produce polarized beams withthe same time structure as the main beam, i.e. , 1312bunches in a 727 µ s long pulse.The electron source design [15] is based on the SLCpolarized electron source, which has demonstarted thatthe bunch charge, polarisation and cathode lifetime pa-rameters are feasible. The long bunch trains of the ILCdo require a newly developed laser system and power-ful preaccelerator structures, for which preliminary de-signs are available. The design calls for a Ti:sapphire laser impinging on a photocathode based on a strainedGaAs/GaAsP superlattice structure, which will produceelectron bunches with an expected polarisation of 85 %,sufficient for 80 % beam polarization at the interactionpoint, as demonstrated at SLAC [76].The positron source poses a larger challenge.In the baseline design, hard gamma rays are producedin a helical undulator driven by the main electron beam,which are converted to positrons in a rotating target.Positrons are captured in a flux concentrator or a quarterwave transformer, accelerated to 400 MeV in two normalconducting preaccelerators followed by a superconduct-ing accelerator very similar to the main linac, before theyare injected into the damping rings at 5 GeV. The helicalundulators produce photons with circular polarisation,which is transferred to the positrons produced in the tar-get, which are longitudinally polarised as a result. Thepositron polarisation thus achieved is 30 %. The E-166experiment at SLAC has successfully demonstrated thisconcept [77], albeit at intensities much lower than fore-seen for the ILC. Technological challenges of the undula-tor source concept are the target heat load, the radiationload in the flux concentrator device, and the dumping ofthe high intensity photon beam remnant.As an alternative, an electron-driven positron sourceconcept has been developed. In the electron-drivenscheme, a 3 GeV electron beam from a dedicated normalconducting linac produces positrons in a rotating tar-get. The electron drive beam, being independent fromthe main linac, has a completely different time structure.Positrons are produced in 20 pulses at 300 Hz with 66bunches each. With this scheme, it takes about 67 msto produce the positrons needed for a single Main Linacpulse with its 1312 bunches, compared to 0 . / s rather than 100 m / s,which reduces the engineering complexity of the targetdesign, in particular the vacuum seals of the rotatingparts. Although not free from its own engineering chal-lenges, such as the high beam loading in the normal con-ducting cavities, the electron driven design is currentlyconsidered to be a low risk design that is sure to work.Aside from the low technical risk, the main advan-tage of the electron driven design is the independence ofpositron production and electron main linac operation,which is an advantage for accelerator commissioning andoperation in general. In particular, electron beam en-ergies below 120 GeV for operation at the Z resonanceor the W W threshold would be no problem. The un-dulator source, on the other hand, offers the possibil-ity to provide beams at the maximum repetition rate of10 Hz given by the damping time in the damping rings of100 ms, whereas the electron driven scheme is limited to6 Hz due to the additional 66 ms for positron production.The main difference between the concepts is the positronpolarisation offered by the undulator source, which addssignificantly to the physics capabilities of the machine.6The physics implications of positron polarization is dis-cussed later in the report, in Secs. 4.10 and 8.3.Both concepts have been reviewed recently [23] insidethe ILC community, with the result that both source con-cepts appear viable, with no known show stoppers, butthey require some more engineering work. The decisionon the choice will be taken once the project has been ap-proved, based on the physics requirements, operationalaspects, and technological maturity and risks. a. Beam polarisation and spin reversal
At the ILC,the electron beam and potentially the positron beam arelongitudinally polarised at the source, i.e. , the polari-sation vector is oriented parallel or antiparallel to thebeam direction. Whenever a longitudinally polarisedbeam of energy E beam is deflected by an angle θ bend ,the polarisation vector undergoes a precession throughan angle θ pol = γaθ bend [78], with the Lorentz factor γ = E beam /m e and the electron’s anomalous magneticmoment a = ( g − /
2. To preserve the longitudinal beampolarisation during the long transport from the sourcethrough the damping rings to the start of the main linac,which involves many horizontal bends, the beam polar-isation vector is rotated into the transverse plane, per-pendicular to the damping ring plane, before the beam istransferred to the damping rings, and rotated back to alongitudinal direction by a set of spin rotators at the endof the RTML (see Sec. 2.3.3). Through the use of two ro-tators, it is possible to bring the polarisation vector intoany desired direction, and compensate any remaining netprecession between these spin rotators and the interac-tion point, so that any desired longitudinal or transversepolarisation at the IP can be provided.To control systematic effects, fast helicity reversal isrequired. This is helicity reversal of each beam indepen-dently, on a pulse to pulse basis, which must be achievedwithout a change of the magnetic fields of the spin ro-tator magnets. For the electron beam, a fast helicityreversal is possible through a flip of the cathode laser po-larisation. For the undulator-based positron source, thephoton polarisation is given by the undulator field. Twoparallel sets of spin rotators in front of the damping ringsare used that rotate the polarisation vector either to the+ y or − y direction. With this scheme, fast kickers canselect a path through either of the two spin rotators andthus provide a fast spin reversal capability [78, 79]. The ILC includes two oval damping rings of 3 . within a time span of only 100 ms, The vertical emittance of the positrons is reduced from (cid:15) y ≈ . µ m to 2 pm. to provide the low emittance beams required at the inter-action point. Both damping rings operate at an energyof 5 GeV.The damping rings’ main objectives are • to accept electron and positron beams at largeemittance and produce the low-emittance beamsrequired for high-luminosity production. • to dampen the incoming beam jitter to providehighly stable beams. • to delay bunches from the source and allow feed-forward systems to compensate for pulse-to-pulsevariations in parameters such as the bunch charge.Compared to today’s fourth generation light sources,the target value for the normalized beam emittance(4 µ m/20 nm for the normalised horizontal / verticalbeam emittance) is low, but not a record value, and it isthus considered to be a realistic goal.The main challenges for the damping ring design areto provide • a sufficient dynamic aperture to cope with the largeinjected emittance of the positrons. • a low equilibrium emittance in the horizontal plane. • a very low emittance in the vertical plane. • a small damping time constant. • damping of instabilities from electron clouds (forthe positron DR) and fast ions (for the electronDR). • a small (3 . − . . . . −
800 mA, where the EC limit that affects the positrons is7assumed to be more stringent. These instabilities arisefrom electrons and ions being attracted by the circulatingbeam towards the beam axis. A low base vacuum pres-sure of 10 − Pa is required to limit these effects to therequired level. In addition, gaps between bunch trains ofaround 50 bunches are required in the DR filling pattern,which permits the use of clearing electrodes to mitigateEC formation. These techniques have been developedand tested at the CESR-TA facility [81]In the damping rings, the bunch separation is only6 . . The Ring to Main Linac (RTML) system [15, Chap. 7] isresponsible for transporting and matching the beam fromthe Damping Ring to the entrance of the Main Linac. Itsmain objectives are • transport of the beams from the Damping Ringsat the center of the accelerator complex to the up-stream ends of the Main Linacs, • collimation of the beam halo generated in theDamping Rings, • rotation of the spin polarisation vector from thevertical to the desired angle at the IP (typically, inlongitudinal direction).The RTML consists of two arms for the positrons andthe electrons. Each arm comprises a damping ring ex-traction line transferring the beams from the dampingring extraction into the main linac tunnel, a long lowemittance transfer line (LTL), the turnaround section atthe upstream end of each accelerator arm, and a spinrotation and diagnostics section.The long transport line is the largest, most costly partof the RTML. The main challenge is to transport thelow emittance beam at 5 GeV with minimal emittanceincrease, and in a cost-effective manner, considering thatits total length is about 14 km for the 250 GeV machine.In order to preserve the polarisation of the particlesgenerated in the sources, their spins are rotated into avertical direction (perpendicular to the Damping Ringplane) before injection into the Damping Rings. A setof two rotators [83] employing superconducting solenoidsallows to rotate the spin into any direction required.At the end of the RTML, after the spin rotation sec-tion and before injection into the bunch compressors (which are considered part of the Main Linac, not theRTML [84]), a diagnostics section allows measurement ofthe emittance and the coupling between the horizontaland vertical plane. A skew quadrupole system is includedto correct for any such coupling.A number of circular fixed-aperture and rectangularvariable-aperture collimators in the RTML provide beta-tron collimation at the beginning of the LTL, in the turnaround and before the bunch compressors. FIG. 12: Artist’s rendition of the ILC Main Linac tunnel.The shield wall in the middle has been removed.c (cid:13)
Rey.Hori/KEK.
The heart of the ILC are the two Main Linacs, whichaccelerate the beams from 5 to 125 GeV. The linac tun-nel, as depicted in Figs. 12 and 13, has two parts, sepa-rated by a shield wall. One side (on the right in Fig. 12)houses the beamline with the accelerating cryomodulesas well as the RTML beamline hanging on the ceiling.The other side contains power supplies, control electron-ics, and the modulators and klystrons of the High-LevelRF system. The concrete shield wall (indicated as a dark-grey strip in in Fig. 12) has a thickness of 1 . . . FIG. 13: Cross section through the Main Linac tunnel. a. RF distribution:
Each cryomodule contains 9cavities, or for every third module, 8 cavities and apackage with a superconducting quadrupole, correctormagnets, and beam position monitor. Nine such mod-ules, with a total of 117 cavities, are powered by 2klystrons and provide 3 . .
29) GeV at a gradient of31 . / m. Table II gives an overview over the unitsthat form the linacs. The waveguide distribution systemallows an easy refurbishment to connect a third klystronfor a luminosity upgrade. The 50 % RF power increasewould allow 50 % higher current through smaller bunchseparation, and longer beam pulses because of a reducedfilling time, so that the number of bunches per pulse andhence the luminosity can be doubled, while the RF pulseduration of 1 .
65 ms stays constant. b. Cryogenic supply:
A 9 module unit forms a cryostring, which is connected to the helium supply line witha Joule-Thomson valve. All helium lines are part of thecryomodule, obviating the need for a separate heliumtransfer line. Up to 21 strings with 189 modules and2 . Unit Comprises Length VoltageCavity 1 .
038 m active length 1 .
25 m 32 . / . / cavities 12 .
65 m 282 /
314 MVRF Unit 4 . . . / .
41 GVCryostring 2 RF units 116 . . / .
82 GVCryounit up to 21 cryostrings 2454 m 53 . / . ◦ shifted inphase (“off crest”) for longitudinal stability, and is given foran average gradient of 31 . /
35 MV / m. A RF unit is poweredby one klystron, each cryostring is connected by a valve boxto the liquid helium supply, and a cryounit is supplied byone cryogenic plant. Total lengths include additional spacebetween components. c. Cost reduction from larger gradients: Figure 14shows the layout of the cryogenic supply system for the 250 GeV machine. At the top, the situation is depictedfor the gradient of 31 . / m with a quality factor of Q = 1 . · , as assumed in the TDR [15]. In thiscase, the access points PM ±
10 would house two cryo-genic plants, each supplying up to 189 cryomodules oran equivalent cryogenic load. In this configuration 6large plants in the access halls plus 2 smaller plants inthe central region would be needed. The bottom pic-ture shows the situation for a gradient of 35 MV / m with Q = 1 . · , as could be expected from successfulR&D. The increased gradient would allow reduction ofthe total number of cryomodules by roughly 10 % from987 to 906. The increased quality factor would reducethe dynamic losses such that 4 cryo plants would providesufficient helium.In general, the accelerator is designed to make gooduse of any anticipated performance gain from continuedhigh gradient R&D, in the case that raising the gradientis seen to be beneficial from an economical point of view,without incurring unwanted technology risk. The Beam Delivery System (BDS) transports the e + /e − beams from the end of the main linacs, focuses them tothe required small beam spot at the Interaction Point(IP), brings them into collision, and transports the spentbeams to the main dumps [15, Chap. 8]. The mainfunctions of the BDS are • measuring the main linac beam parameters andmatching it into the final focus. • protecting beamline and detector from mis-steeredbeams . • removing large amplitude (beam–halo) and off–momentum particles from the beam to minimizebackground in the detector. • accurately measuring the key parameters energyand polarisation before and after the collisions.The BDS must provide sufficient diagnostic and feedbacksystems to achieve these goals.The BDS is designed such that it can be upgraded toa maximum beam energy of 500 GeV; components suchas the beam dumps, that are not cost drivers for theoverall project but would be cumbersome to replace later,are dimensioned for the maximum beam energy from thebeginning. In other places, such as the energy collimationdogleg, those components necessary for 125 GeV beamoperation are installed and space for a later upgrade isreserved. On the electron side, the protective fast beam abort system isactually located upstream of the positron source undulator. FIG. 14: Cryogenic layout for a gradient of 31 . / m (top) and 35 MV / m (bottom) [2]. “Module space” indicates howmany cryomodules can be physically installed, “cryomodules” and “RF unit” indicates the number of actually installedmodules and klystrons (one klystron per 4.5 cryomodules). “E gain” indicates the energy gain in GeV. “BC”, “ML”, “e+inj”, “e- inj” and “UND” refer to the sections with need for liquid helium: bunch compressor, main linac, 5GeV boosters inthe positron and electron source, and the positron source undulator section, respectively. PM ± , ,
12 refer to access halllocations, “C” to cryo plants; meter numbers on top indicate the length of the corresponding section.
Overall, the BDS is 2254 m long from the end of themain linac (or the undulator and target bypass insert ofthe positron source on the electron side, respectively) tothe IP. a. Diagnostics and collimation section:
The BDSstarts with a diagnostics section, where emittance, en-ergy and polarisation are measured and any coupling be-tween the vertical and horizontal planes is corrected by aset of skew quadrupoles. The energy measurement is in-corporated into the machine protection system and can, e.g. , extract off-momentum bunches caused by a klystronfailure in the main linac that would otherwise damagethe machine or detector. An emergency dump [21] is di-mensioned such that it can absorb a full beam pulse at 500 GeV, sufficient for 1 TeV operation.The diagnostics section is followed by a collimationsystem, which first removes beam halo particles (beta-tron collimation). Then, off-momentum particles are re-moved. In this energy collimation section, sufficient dis-persion must be generated by bending the beam in a dog-leg, while avoiding excessive synchrotron radiation gen-eration in dispersive regions that leads to an increase ofthe horizontal emittance. This emittance dilution effectgrows as E at constant bending radius for the nor-malised emittance, and determines the overall length ofthe energy collimation section for a maximum 500 GeVbeam energy to about 400 m.0 b. Final focus with feedback system and crab cavities: The final focus system demagnifies the beam to the re-quired spot size of 516 × . by means of a finalquadrupole doublet. Even the relatively small energyspread of ≈ . µ s and 554 ns,respectively) are large enough to allow corrections be-tween pulses as well as within a bunch train (intra-train feedback). Beam-beam offsets of a fraction of thebeam size lead to a measurable deflection of the out-going beams,and these measurements are used to feedfast stripline kickers that stabilize the beam. Finally, the3 . c. Test results from ATF2: The Accelerator TestFacility 2 (ATF2) was built at KEK in 2008 as a testbench for the ILC final focus scheme [14, Sec. 3.6]. Itsprimary goals were to achieve a 37 nm vertical beam sizeat the interaction point (IP), and to demonstrate beamstabilisation at the nanometre level [86, 87]. After scal-ing for the different beam energies (ATF2 operates at E beam = 1 . σ ∗ y = 5 . d. Machine detector interface (MDI): The ILC isconfigured to have two detectors that share one interac-tion point, with one detector in data taking position atany time, in a so–called “push–pull” operation [14, Sec.8.4]. Both detectors are mounted on movable platformsthat allow an exchange of the detectors within approxi-mately 24 hours.In the push–pull scheme, the innermost final focusquadrupole “QD0”, a slim, superconducting magnetpackage combined with a sextupole for local chromatic-ity correction, is installed within the detectors. The other
FIG. 15: Beamsizes achieved at the Accelerator Test Facility2 (ATF2) as a function of time [92]. The latest result(41 nm [88]) is within 10 % of the goal beam size of 37 nm. part of the final focus doublet (“QF1”) is located outsidethe detector on a bridge, and does not move with thedetector. Since the TDR, the free space L ∗ between in-teraction point and the QD0 edge has been harmonisedto a common value of L ∗ = 4 . e. Main dump: The main beam dumps [15, Sect.8.8] are rated for a maximum beam power of 17 MW [21],enough for a 1 TeV upgrade of the accelerator. The maindump design is based on the successful SLAC 2 . Be produced from spallation processes. The entry win-dow is another component that has to be carefully de-signed. f. Measurement of beam energy, luminosity, andbeam polarisation:
Two energy spectrometers, one lo-cated 700 m upstream of the IP, the other 55 m down-stream, provide independent and complementary mea-surements of the beam energy with an accuracy of100 ppm [94].The luminosity is measured to 10 − accuracy from lowangle Bhabha scattering in the so–called LumiCal (seeSect. 6.2.5) at polar angles from 30 to 90 mrad. Addi-tional calorimeters (BeamCal) in the region 5 to 30 mradprovide a fast signal that is sensitive to the beam sizesand offsets of the colliding beam, and that can thus beused for their tuning, as part of an intra-beam feedbacksystem (see Sec. 2.3.5).Beam polarisation is measured with 0 .
25 % accuracy1by means of Compton scattering: electrons that scatteroff green or infrared light laser photons lose enough en-ergy that they can be detected in a spectrometer; theirmomentum spectrum is used to fit the beam polarisa-tion [95]. Two such polarimeters are located 1800 m up-stream and 150 m downstream of the IP, which allows tointerpolate the precise polarisation at the IP and con-trol the systematics, including effects from precession ofthe polarisation vector by transverse fields and depolar-ising effects in the interaction, which lead to a sizeablevariation of the polarisation within the bunch during thecollision (see Sect. 8.3.1).
Given the high initial investment for a facility aslarge as the ILC, it is mandatory to have an interestingphysics programme for several decades, with the possi-bility to adapt the programme to the needs arising fromthe knowledge obtained by the LHC, the ILC itself, allother particle physics experiments, and other domainsof physics such as cosmology. Several options exist forupgrades of the ILC in terms of energy, luminosity, andbeam polarisation.
The obvious advantage of a linear collider is its upgrade-ability in energy. Basically, the main linacs can be ex-tended as far as desired, at constant cost per added beamenergy, with some added cost for the relocation of theturn arounds and bunch compressors. Additional costsarise when the beam delivery system (BDS), includingthe beam dumps, has to be extended to handle the in-creased beam energy. The current ILC BDS is designedto be easily upgradeable for centre of mass energies upto 1 TeV at minimal cost.Depending on the actual gradient achieved for the con-struction of the ILC, up to 171 cryomodules could beinstalled in addition to those needed to reach 250 GeV,which would increase the centre-of-mass energy by about54 GeV to around 304 GeV, as Fig. 14 shows, and possi-bly require the installation of two additional cryo plants.A further energy upgrade would require extension ofthe tunnel. The Kitakami site can accommodate a totalaccelerator length of at least 50 km, more than enoughfor a 1 TeV centre–of–mass energy. Any extension of theaccelerator would proceed by adding new cryomodules atthe low energy (upstream) ends of the accelerator. Thereis no need to move modules already installed.An upgrade would likely proceed in two phases: apreparation phase while the accelerator is still operatedand produces data, and a refurbishment phase where theaccelerator is shut down.During the preparation phase, the necessarycomponents—in particular the cryomodules, klystrons,and modulators—would be acquired and built. At thesame time, civil engineering would proceed with the excavation of new access tunnels, underground halls, andthe main tunnel. Recent studies conducted during roadtunnel construction in the Kitakami area, in the samerock formation as foreseen for the ILC, indicate that thelevel of vibrations caused by tunnelling activities wouldallow to bring the new tunnels quite close to the existingones before machine operation would be affected [96],minimising the shutdown time necessary.During the installation phase, the newly built tunnelswould be connected to the existing ones, the beam linesat the turn-around and the wiggler sections of the bunchcompressors would be dismantled, and the new cryomod-ules would be installed as well as the new turn-aroundand bunch compressors. At the same time, any neces-sary modifications to the positron source and the finalfocus can be made. With the cryomodules ready for in-stallation at the beginning of the shut down period, it isestimated that the shutdown could be limited to about ayear for an energy upgrade.
The luminosity of the ILC can be increased by increas-ing the luminosity per bunch (or per bunch charge), orincreasing the number of bunches per second [97].Increasing the luminosity per bunch requires a smallervertical beam spot size, which may be achieved by tighterfocusing and/or smaller beam emittance. Studies in-dicate that with enough operating experience, there ispotential for a further luminosity increase. This routeto increased luminosity is, however, invariably linked tohigher beam disruption, which brings a risk of a lumi-nosity loss due to mis-steering the beam. Thus, a veryaccurate feedback system is required.The ILC design also has the potential to increase thenumber of colliding bunches per second, by doubling thenumber of bunches per pulse, and possibly by increasingthe pulse repetition frequency.Doubling the number of bunches per pulse to 2625would require a smaller bunch spacing, requiring the in-stallation of 50 % more klystrons and modulators. Sincethe RF pulse length of 1 .
65 ms is unchanged, the cryo-genic load is essentially unchanged. Doubling the num-ber of bunches would double the beam current in thedamping rings. For the positron damping ring, this maysurpass the limitations from electron cloud (EC) insta-bilities. To mitigate this risk, the damping ring tunnel islarge enough to house a third damping ring, so that thepositron current could be distributed over two rings.The pulse repetition rate (5 Hz in the baseline configu-ration) is limited by the available cryogenic capacity, thedamping time in the damping rings, and the target heatload in the positron source target. The damping rings aredesigned for a 100 ms damping time and thus capable ofa repetition rate of up to 10 Hz, twice the nominal rate.Operation at an increased repetition rate would be pos-sible if after an energy upgrade the machine is operatedbelow its maximum energy (e.g., 250 GeV operation of a2500 GeV machine for a larger low-energy data set), or ifadditional cryogenic capacity is installed.
The baseline design foresees at least 80 % electron polar-isation at the IP, combined with 30 % positron polarisa-tion for the undulator positron source. At beam ener-gies above 125 GeV, the undulator photon flux increasesrapidly. Photon polarisation is maximal at zero emis-sion angle; it is decreased and even inverted at larger an-gles. Thus, collimating the surplus photon flux at largeremission angles increases the net polarisation. Studiesindicate that 60 % positron polarisation at the IP maybe possible at 500 GeV centre–of–mass energy with theaddition of a photon collimator.
In 2014, the ILC Strategy Council announced the re-sult of its candidate site evaluation for the best possibleILC site in Japan [98]. The evaluation was conductedby a number of Japanese experts from universities andindustry, and reviewed by an international commitee. Itconsidered technical as well as socio-environmental as-pects, and concluded that the candidate site in the Ki-takami region is best suited for the ILC.
FIG. 16: The Kitakami candidate site for the ILC [99].
The site (Fig. 16) is located in the Japan’s northernTohoku region, not far from Sendai with its interna-tional airport, in the prefectures of Iwate and Miyagi.The closest cities are Ichinoseki, Oshu, and Kitakami,which all offer Shinkansen (bullet train) access to Sendaiand Tokyo. The closest harbour is in the city of Kesen-Numa. The coastal region in this area was severely hitby the great Tohoku earthquake in 2011. Both prefec-tures are supportive of the ILC project and view it asan important part of their strategy to recover from theearthquake disaster. The Kitakami site was largely selected because of itsexcellent geological condition. The proposed ILC trajec-tory lies in two large, homogeneous granite formations,the Hitokabe granite in the north and Senmaya graniteto the south. The site provides up to 50 km of space,enough for a possible 1 TeV upgrade or more, dependingon the achievable accelerating gradient. Extensive geo-logical surveys have been conducted in the area, includ-ing boring, seismic measurements, and electrical mea-surements [100], as shown in Fig. 17. The surveys showthat the rock is of good quality, with no active seismicfaults in the area.Earthquakes are frequent throughout Japan, and theaccelerator and detectors need proper supports that iso-late them from vibrations during earthquakes and microtremors [101]. Proven technologies exist to cope with allseismic events, including magnitude 9 earthquakes suchas the great Tohoku earthquake.Vibration measurements taken during the constructionof a road tunnel show that accelerator operation would bepossible during the excavation of a tunnel for an energyupgrade [102].
0 10 20 30 40 50 km Electromagnetic prospectingSeismic prospectingGeology SENMAYA ORIKABE seismic prospecting Seamless Digital Geological Map of Japan (1:200,000)
HITOKABE
FIG. 17: Geological situation at the Kitakami site.
For the Technical Design Report, the construction costof the ILC accelerator was carefully evaluated from a de-tailed, bottom–up, WBS (Work Breakdown Structure)-based cost estimation [15, Sect. 15]. The TDR estimatedistinguishes two cost categories: Value accounts for ma-terials and supplies procured from industry and is givenin ILCU (ILC Currency Unit, where 1 ILCU = 1 US$ in2012 prices), and Labour accounts for work performedin the participating institutions and is given in person–hours or person–years . One person–year corresponds to 1700 working hours. Common8% Electron Source4% Positron Source6%Damping Rings10%
RTML11%
Main Linac50%
BDS7% IR4%
ACCELERATOR SYSTEMS250GEV, 35MV/M
CFS-Civil construction21%CFS-other15%Cavities and Cryomodules w/o SC material22%SC material2%HLRF9%Cryogenics6%Magnets and Power Supplies9%Controls and LLRF5%Instrumentation3% Vacuum2% Other6%
TECHNICAL SYSTEMS250 GEV, 35MV/M
FIG. 18: Breakdown of Value costs into accelerator systems (left) and technical systems (right) for the 250 GeV ILCaccelerator, assuming that cost reduction measures are successful and a gradient of 35 MV / m can be reached. The Value of acquired goods reflects its worth in thelocal currency of the purchasing institution. There-fore, conversion of Value between currencies is performedbased on Purchasing Power Parities (PPP), which areregularly evaluated and published by the OECD [103,104], rather than currency exchange rates. The PPP val-ues reflect local price levels and thus depend on the typeof goods and the country, but fluctuate significantly lessthan currency exchange rates. Therefore, conversionsfrom ILCU to other currencies cannot be made on thebasis of exchange rates to the U.S. dollar, but on PPPvalues.The TDR estimate covers the cost of the acceleratorconstruction, assumed to last 9 years plus one year ofcommissioning. It includes the cost for the fabrication,procurement, testing, installation, and commissioning ofthe whole accelerator, its components, and the tunnels,buildings etc. , and the operation of a central laboratoryat the site over the construction period. It does not, how-ever, cover costs during the preparation phase precedingthe start of construction work (“ground breaking”), suchas design work, land acquisition, infrastructure (roads,electricity, water) for the site.Based on the TDR cost estimate, an updated cost es-timate was produced for the 250 GeV accelerator. Thisupdated cost estimate includes the cumulative effect ofthe changes to the design since the TDR (see Sect. 2.1),and evaluates the cost for the reduced machine by ap-plying appropriate scaling factors to the individual costcontributions of the TDR cost estimate.The resulting Value estimate for the ILC accelerator at250 GeV is 4 , − ,
260 MILCU [2] in 2012 prices, wherethe lower number assumes a cavity gradient of 35 MV / m,while the higher number is based on the TDR number of 31 . / m. In addition, 17 ,
165 kh (thousand person-hours) are required of institutional Labour.In 2018, the ILC Advisory Panel of the Japanese Min-istry of Education, Culture, Sports, Science and Tech-noloy (MEXT) concluded its review of the ILC [105].For this review, costs were evaluated in Japanese Yen in2017 prices, taking into account the local inflation forgoods and construction costs. For the purpose of thisestimate, also the Labour costs were converted to Yento yield 119 . (cid:85) , resulting in a total range of the ac-celerator construction cost of 635 . − . (cid:85) , wherethe range covers uncertainties in the civil constructioncosts (18 G (cid:85) ) and of the gradient (49 . (cid:85) ). For thethis estimate, conversion rates of 1 US$ = 100 JP (cid:85) and1 e = 1 .
15 US$ were assumed.Operation costs of the accelerator and the centrallaboratory are estimated to be 36 . − . (cid:85) (about318 −
341 M e ) per year.
3. ILC RUNNING SCENARIOS
One of the key advantages of e + e − colliders is the abil-ity to collect individual datasets at a series of differentcenter-of-mass energies and beam polarisation settings.While each measurement one might wish to make has itsown prefered data-taking mode, the combination withdatasets collected at other beam energies and/or beampolarisations provides a unique robustness against sys-tematic uncertainties. For example, a recent PhD the-sis [106] studied Dark Matter searches with considerationof non-neglibigle systematic uncertainties and showedthat one obtains better results by sharing a given amountof total integrated luminosity between datasets with dif-4 years ] - I n t eg r a t ed Lu m i no s i t y [f b Lu m i no s i t y U pg r ade E ne r g y U pg r ade ILC, Scenario H20-staged
ECM = 250 GeVECM = 350 GeVECM = 500 GeV
FIG. 19: The nominal 22-year running program for thestaged ILC, starting operation at 250 GeV with the currentbaseline beam parameters for the 250 GeV runs [4]. ferent beam polarisations rather than by investing thesame total amount of luminosity into the (statistically)most favourable polarisation configuration.Any physics projection will therefore depend on the ex-act running scenario, i.e. the ensemble of the integratedluminosities collected at the individual center-of-mass en-ergies with the various polarisation settings. The ILCas currently under political consideration in Japan willbe limited to a center-of-mass energy of 250 GeV. Al-ready at this energy, the ILC offers a formidable physicsprogramme, which is described in detail in the followingSec. 4. The intrinsic upgradability to higher energies,however, is a key feature of a linear collider, which clearlysets it apart from any circular e + e − collider. In orderto illustrate the full potential of the ILC, the upgradeoptions introduced in Sec. 2.4 are therefore included inthe running scenarios. The timelines presented here arebased on technological possibilities and physics require-ments only, and do not include funding considerations.For the physics conclusions given in this paper, we haveassumed the energy and luminosity evolution of the ILCshown in Fig. 19. At each energy, the time is sharedamong the various choices for beam polarization in themanner explained in Sec. 3.2. The full physics program isprojected to take 22 years, including a realistic learningcurve for the establishment of luminosity and scheduleddowntimes for luminosity and energy upgrades. In thisschedule, the ILC would accumulate 2 ab − at 250 GeVby year 11. It woud then add datasets of 0.2 ab − at350 GeV and 4 ab − at 500 GeV by year 22.The interplay between different datasets has been stud-ied in detail in [107], with a special focus on the opti-misation of the Higgs precision measurements, resultingin a standard running scenario for ILC physics projec-tions. The time evolution of this running scenario hasbeen adapted to the staged construction of the ILC asfirst presented in [4].In this section, we will discuss the considerations that have led to the choice of this running scenario, the evolu-tion of this scenario in accord with the design of the ILCaccelerator, and the flexibility of the plan to respond tochanges in machine specifications or physics discoveries. The three center-of-mass energies for ILC best moti-vated by our current knowledge are: • √ s = 250 GeV for collecting data near the thresh-old of the Higgsstrahlungs process, • √ s = 350 GeV for scanning the threshold for topquark pair production, and • √ s = 500 GeV or somewhat above for studying tt production in the continuum and enabling ttH and ZHH production.Table III gives the total integrated luminosities foreseenat these energies for three alternative running scenarios.These scenarios are described in [107], which presented adetailed evaluation of these and other possibilities. Forcomparison, the integrated luminosities assumed in theSnowmass community study [108] is given in the last col-umn. Since 2015, the scenario H20 has been the referencescenario for ILC physics projections. (cid:82) L dt [fb − ] √ s G20 H20 I20 Snow250 GeV 500 2000 500 1150350 GeV 200 200 1700 200500 GeV 5000 4000 4000 1600TABLE III: Proposed total target integrated luminosities for √ s = 250, 350, 500 GeV based on 20 “real-time” years ofILC operation under scenarios G20, H20 and I20. The totalintegrated luminosities assumed for Snowmass are listed forcomparison based on 13.7 “real-time” years. From [107]. It must be stressed, however, that flexibility in the runplan remains one of the key assets of the ILC. This plancan be adjusted whenever new insights, discoveries eitherfrom the (HL-)LHC or from the ILC itself, require us todo so. In particular, the center-of-mass energy of the ILCcan always be lowered from the nominal maximum energywithout loss of efficiency, as long as the electron beam en-ergy remains sufficiently high for positron production. Infact, the operation of the SCRF cavities below the maxi-mum gradient saves significant cryogenic and RF power,which in turn can be invested into higher instantaneousluminosity.Future e + e − colliders could also provide importantphysics measurements at other center-of-mass energies.Physics goals that motivate other choices are the high-statistics study of Z and W , the exploration of thethresholds for any new color-singlet particles that might5appear in the ILC energy region, and data-taking at ad-ditional center of mass energies to optimize the determi-nation of Effective Field Theory parameters. The lowercenter-of-mass energies could be realized by doubling therepetition rate of the electron linac to 10 Hz and addinga by-pass around the positron source for every secondbunch train. Today, however, the priority of these issuesseems lower than that for the abovementioned three en-ergies. Therefore they are not explicitly included in thecurrent run plan of the ILC or in the current set of ma-chine parameters. Over a longer term, we plan to extendthe linac to reach energies of 1 TeV or higher. Table IVlists target integrated luminosities approriate to physicsstudies at these additional energies. √ s
90 GeV 160 GeV 1 TeV (cid:82) L dt [fb − ] 100 500 8000TABLE IV: Proposed total target integrated luminosities forother √ s . From [107]. At center-of-mass energies of up to 500 GeV, the ILCbeams are foreseen to be polarised with absolute valuesof at least 80% for the electrons and at least 30% for thepositrons. At 1 TeV, the positron polarisation will reachat least 20%. As an upgrade option, the positron polar-isation can be increased to 60% for center-of-mass ener-gies around 500 GeV; this is discussed in Sec. 2.4.3. Theaccelerator design comprises sets of spin rotators whichin principle allow one to prepare any desired direction ofthe polarisation vectors at the IP. However in the detailedrunning scenarios, we consider only longitudinal polarisa-tion. The sign of the beam polarisations can be flipped ona train-by-train basis. This allows us to collect datasetswith different helicity configurations quasi-concurrentlycompared to the typical time scales of changes in the ac-celerator or detector configuration, calibration and align-ment. In a joint analysis of these datasets, large parts ofthe experimental systematic uncertainties cancel. This isparticularly important to minimize the systematic errorsin the measurement of the left-right polarization asym-metry, a quantity that carries a great deal of informationfor every process that will be studied at the ILC. Butthis idea has many other applications. The joint inter-pretation of the different datasets allows us to treat manysystematic effects as nuisance parameters in global fits,and thereby to measure and subtract these effects [109].The role of positron polarisation specifically at an ini-tial 250-GeV stage of the ILC has been discussed in detailin a recent document [110]. In the case of a global fit topolarised total and differential cross-sections of variouselectroweak processes, it is shown there that the uncer-tainties on some observables increase by up to a factorof 10 in the absence of positron polarisation due to thelack of redundancies required for ultimate control of sys-tematic uncertainties (see Sec. 8.3). As we will see in Sec. 4.6, the left-right asymmetry A LR ( HZ ) of the Hig-gsstrahlungs cross section plays an important role in ourtechnique for obtaining a model-independent fit to Higgscouplings. Although the measurement of the absolutenormalization of the Higgsstrahlungs cross section wasnot explicitly included in the study summarized in [110],analogous deteriorations would also be expected for thisquantity.A part of the power of positron polarisation is thatit allows one to collect four independent data setswith different mixtures of the physics reactions understudy. Tables V through VIII give our standard as-sumptions for the sharing of the total integrated lu-minosity (c.f. Tab. III and IV) between the four pos-sible beam helicity combinations. Due to the impor-tance of A LR ( HZ ) [3, 111] noted above, the sharing for250 GeV, which was originally foreseen [107] to emphasizethe sgn( P ( e − ) , P ( e + )) = ( − , +) configuration, is now ad-justed to provide equal amounts of luminosity for ( − , +)and (+ , − ) [3, 4].These integrated luminosities and polarisation config-urations, especially as specified in Tab. VI for the H20running scenario, define the reference scenario for all ILCphysics projections. The order in which the various en-ergies are surveyed will of course depend on the machineevolution and staging plan. fraction with sgn( P ( e − ) , P ( e + )) =(-,+) (+,-) (-,-) (+,+) √ s [%] [%] [%] [%]250 GeV (2015) 67.5 22.5 5 5250 GeV (update)
45 45 P ( e − ) , P ( e + )) =(-,+) (+,-) (-,-) (+,+) √ s [fb − ] [fb − ] [fb − ] [fb − ]250 GeV (2015) 1350 450 100 100250 GeV (update)
900 900
100 100350 GeV 135 45 10 10500 GeV 1600 1600 400 400TABLE VI: Integrated luminosities per beam helicityconfiguration resulting from the fractions in table V inscenario H20. The update of the luminosity sharing for250 GeV originates from the importance of the left-rightasymmetry of the Higgsstrahlung cross section in theEFT-based Higgs coupling fit. fraction with sgn( P ( e − ) , P ( e + )) =(-,+) (+,-) (-,-) (+,+) √ s [%] [%] [%] [%]90 GeV 40 40 10 10160 GeV 67.5 22.5 5 51 TeV 40 40 10 10TABLE VII: Relative sharing between beam helicityconfigurations proposed for low energy and 1 TeV running.From [107].integrated luminosity with sgn( P ( e − ) , P ( e + )) =(-,+) (+,-) (-,-) (+,+) √ s [fb − ] [fb − ] [fb − ] [fb − ]90 GeV 40 40 10 10160 GeV 340 110 25 251 TeV 3200 3200 800 800TABLE VIII: Integrated luminosities per beam helicityconfiguration resulting from the fractions in table VII.From [107]. The possible real-time evolution of the integrated lu-minosity was studied in detail in [107]. It is importantto note that the plans given in that study assumed thatthe full 500 GeV machine would be available from thebeginning. With the introduction of a staged construc-tion plan for the ILC, the time ordering of different runsneeded to be adjusted. However, the details of trade-offsbetween scenarios is most fully documented in [107], sowe will first review that study and the logic of its con-clusions. After this, we will describe our current plan forthe run scenario including the constraints from staging.
In the study [107], the peak luminosities used for eachcentre-of-mass energy are based on the numbers pub-lished in the ILC TDR [14]. But then, the plans tookadvantage of the reduced linac electrical power and cryo-genic loads when operating the full 500 GeV machine atlower gradients. This in particular allows 10-Hz and 7-Hz running, respectively, at the 250 GeV and 350 GeVcentre-of-mass energies. In addition, a luminosity up-grade (from 1312 to 2625 bunches per pulse) was beenconsidered; this could require the installation of an addi-tional positron damping ring, as described in Sec. 2.4.2.More specifically, the study [107] made the followingassumptions: • A full calendar year is assumed to represent eightmonths running at an efficiency of 75% as assumedin the ILC RDR [112]. This corresponds approxi-mately to Y = 1 . × seconds of integrated run-ning, thus 60% more than a “Snowmass year” of10 seconds. • The start of “Year 1” is the start of running forphysics. After the end of construction, there isone year foreseen for machine commissioning only,which is not shown on the plots. • A ramp-up of luminosity performance, defined asa set of yearly ramp factors f ≤
1, is in generalassumed after: (a) initial construction and ‘year0’ commissioning; (b) a downtime for a luminosityupgrade; (c) a change in operational mode whichmay require some learning curve ( e.g. , going to 10-Hz collisions). • If the peak instantaneous luminosity is L , then thenominal integrated luminosity for any given calen-dar year is (cid:82) L dt = f × L × Y , where f is the rampfactor associated with that year. • The peak instantaneous luminosities are those cor-responding to the TDR beam parameters at 250,350 and 500 GeV, as shown in Tab. I. • For the initial physics run after construction andyear 0 commissioning, the RDR ramp of 10%, 30%,60% and 100% over the first four calendar years isalways assumed. • The ramp after the shutdown for installation ofthe luminosity upgrade is assumed to be slightlyshorter (10%, 50%, 100%) with no year 0. • Going down in centre of mass energy from 500 GeVto 350 GeV or 250 GeV is assumed to have no rampassociated with it, since there is no modification(shutdown) of the machine. • Going to 10-Hz operation at 50% gradient does as-sume a ramp however (25%, 75%, 100%), since 10-Hz affects the entire machine including the damp-ing rings and sources.Under these assumption, a possible real-time scenariofor collecting the integrated luminosities of the H20 sce-nario (c.f. Tab III) is shown in Fig. 20. Since it wasassumed that the full 500-GeV machine would be avail-able from the start, the first foreseen run was intendedto collect a dataset of 500 fb − at √ s =500 GeV in orderto observe for the first time ever tt production via theelectroweak force, to survey the full kinematic reach forpossible new particles and, last but not least, to collecta comprehensive set of Higgs precision data, with similarcontributions from the Higgsstrahlung and W W fusionprocesses (see Fig. 44).After this general-purpose survey at the maximum en-ergy, it was planned to collect dedicated datasets at lowerenergies, at the tt production threshold, for a precisiondetermination of a theoretically well-defined top mass,and somewhat above the ZH production threshold, nearthe maximum of the cross section. The ZH measure-ments at 250 GeV would be a very important componentof the program even under the assumption that energies7 years ] - I n t eg r a t ed Lu m i no s i t y [f b Lu m i no s i t y U pg r ade ILC, Scenario H20
ECM = 250 GeVECM = 350 GeVECM = 500 GeV
FIG. 20: The nominal 20-year running program for the500-GeV ILC [107]. of 500 GeV are immediately available. This is true for tworeasons. First, in Higgsstrahlung production, each Higgsboson is tagged by the recoil Z . There are many mea-surements that rely on this tag to identify Higgs bosonsor to measure absolute rates without the need to make as-sumptions about the Higgs decay modes. These includethe measurement of the normalised total cross sectionfor the Higgsstrahlung process, the measurement of ab-solute branching ratios of the Higgs boson and the searchfor invisible and exotic decays. At 500 GeV, far abovethe threshold, recoil measurements become less charac-teristic, due to the more substantial ISR and increasedamount of beamstrahlung with respect to 250 GeV, andare subject to additional backgrounds. Other measure-ments depend on precise reconstruction of the kinematicsof the e + e − → ZH process. For example, the ultimateprecision on the Higgs mass will be obtained using thekinematics of Z recoil. The search for deviations fromthe SM predictions for Higgs decays requires as input avery precise value of this mass; see Sec. 8.2.1. Anotherreaction that depends crucially on precise kinematic mea-surements is the CP analysis of the H → τ + τ − decay,discussed in Sec. 8.2.8.For a 500 GeV machine running at 250 GeV, the lumi-nosity can be straightforwardly increased by a factor of2 from the TDR value by the increase of the repetitionrate for bunch trains from 5 to 10 Hz. This improvementwas incorporated in the plan H20 shown in Fig. 20 evenat the initial stage of 250 GeV running.The H20 plan also included provision for an additionalluminosity upgrade by doubling the number of bunchesin each bunch train. This upgrade requires machine im-provements as described in Sec. 2.4.2, and after these im-provements all further data would be taken in this mode.This would give a total 4 ab − data sample at 500 GeV.A sample of this size is required for meaningful preci-sions on the top Yukawa coupling and on the Higgs self-coupling. These measurements remain by far statisticallylimited and thus would profit from any further increase of the luminosity. In case of the top Yukawa coupling, itwas noted that it is absolutely crucial to reach 500 GeV,since already at 490 GeV, thus when falling short of thetarget energy by only 2%, the precision of the measure-ment would worsen by nearly a factor of 2. On the otherhand, a moderate increase of the center-of-mass energyby 6% to 530 GeV would improve the precision on thetop-Yukawa coupling by a factor of 2. This should beconsidered in the planning of the energy upgrade of aninital 250 GeV machine, see also discussion in Sec. 2.4.1.Finally the H20 scenario planned a run at 250 GeV,now with 4 times the TDR luminosity, to finish the col-lection of a 2 ab − data set. This run would provide theultimate precision on the Higgs boson mass and the to-tal ZH cross section. It should be stressed again thatthe current focus on three fixed center-of-mass energiesdoes not preclude running at any other desired interme-diate energy, e.g. for scanning the production thresholdof newly discovered particles.At the end of this 20 year program, we envision a fur-ther doubling of the energy to 1 TeV. This upgrade waspresented already in the ILC TDR and is reviewed inSec. 2.4.1. This energy upgrade could possibly be pre-ceeded by a run at the Z pole if it is required by thephysics. With the introduction of the staging plan for the ILC ma-chine construction, it was necessary to change the timeordering of the various energy steps in the program de-scribed in the previous subsection. However, the totalintegrated luminosities to be collected at each center-of-mass energy, which were already optimized for thephysics goals, were left untouched. Thus, all physicsprojections based on the H20 scenario remained valid -albeit the results will arrive in a different time order.Figure 21 shows the original plan for the time evolutionof the staged H20 scenario. The assumptions differ fromthose listed in the previous subsection in the followingpoints: • No 10 Hz operation is assumed since in the 250 GeVmachine the cryomodules will be operated at fullgradient and thus no spare cryo- and RF-power isavailable. Technically, it would be possible to in-crease the repetition rate (and thus the luminosity)at any time provided that resources for installingthe additional cryo- and RF-power and for cover-ing the higher operation costs could be found. Thisoption is not included in the staging scenario. • The luminosity upgrade by doubling the number ofbunches per train (c.f. Sec. 2.4.2) is a smaller in-vestment than the energy upgrade and will there-fore happen first. In this plan, the second positrondamping ring and the additional cryo- and RF-power needed for the luminosity doubling would8 years ] - I n t eg r a t ed Lu m i no s i t y [f b Lu m i no s i t y U pg r ade E ne r g y U pg r ade ILC, Scenario H20-staged-orig
ECM = 250 GeVECM = 350 GeVECM = 500 GeV
FIG. 21: The nominal 26-year running program for thestaged ILC, starting operation at 250 GeV without thepossibility to operate at 10 Hz [4]. The integratedluminosities are the same of for the original H20 scenario. already be installed at the start of 500 GeV opera-tion. Then the entire 500 GeV run would be doneat 2 times the TDR luminosity. • The energy upgrade (described in Sec. 2.4.1) re-quires only a relatively short machine shutdown ofabout one year, since major parts of the new tunnelcan be constructed and the new parts of the ma-chine can be installed without disturbing the op-eration of the 250-GeV machine. A shutdown isnecessary only during the construction of the con-nections of the new parts of the machine to theolder ones. • After the energy upgrade the same ramp fractionsas for a completely new machine are assumed, thus10%, 30%, 60% and 100% over the first four calen-dar years.With these assumptions, the real-time for realizationof the full H20 program increases from 20 to 26 years,mostly due to the much longer time to collect the 2 ab − at 250 GeV without 10 Hz operation.In order to mitigate the absence of the 10 Hz opera-tion, which would require additional investments beyondthe minimal 250-GeV machine, cost neutral ways to in-crease the luminosity at 250 GeV have been studied, asdiscussed in Sec. 2. In 2017, a new set of beam parame-ters for the 250-GeV ILC was officially adopted [22]. It isthis parameter set that is shown in the column “initial”of Tab. I. The 65% increase in instantaneous luminosityw.r.t. the TDR parameters is achieved by reducing thehorizontal emittance by a factor of 2. This leads to alarger luminosity in each bunch crossing and thus to anincrease of beamstrahlung, background from e + e − pairsand pile-up from low- p t γγ → hadrons events. Neitherthese effects, nor the slightly wider luminosity spectrumwhich results from the increased beamstrahlung are in-cluded in the physics case studies presented in the follow- ing sections, since no new Monte-Carlo samples could beproduced (and analysed) since the new beam parametersbecame available. However, even with the new beam pa-rameters the background conditions at 250 GeV do notbecome worse than what is expected at 500 GeV, a casealready studied in detail. The ILC detectors have ac-tually been designed for high performance in the moredifficult beam conditions at 1 TeV. Therefore, the im-pact of the new beam parameters on the majority of thephysics analyses is expected to be minor. The analysismost strongly affected is the mass measurement of theHiggs boson via the leptonic recoil method, described inSec. 8.2.1. For this analysis, the new beam parametershave been estimated to result in a relative degradationof the ultimate precision on the Higgs mass by about25% [113] compared to the same amount of total lumi-nosity collected with the TDR beam parameters. Thisstill corresponds to an impressive Higgs mass measure-ment to better than 20 MeV.We have already shown in Fig. 19 the default runningscenario for the staged ILC based on the new beam pa-rameters for 250 GeV [22]. Compared to Fig. 21, thetotal run time shortens from 26 years to 22 years, thusrecovering about 2/3 of the original increase in runningtime. A full-scale Monte-Carlo production with the newbeam parameters and based on the ILD detector conceptis planned for 2019.None of the running scenarios explicitly includes theoption to increase the positron polarisation to 60% whenoperating at a center-of-mass energy of 500 GeV. Nu-merous studies [106, 110, 114–116] have shown that allphysics measurements will profit from the correspondingincreases in effective luminosity and effective polarisa-tion. In this respect, all physics projections for 500 GeVare still quite conservative.
4. PHYSICS CASE – 250 GEV
The core of the physics case for the ILC is to makehigh-precision measurements of the properties of theHiggs boson. The Higgs field has a central role in theSM. It is responsible for the masses of all known elemen-tary particles. It is also responsible for those aspects ofthe SM that are hardest to understand—-the presence ofspontaneous gauge symmetry breaking, and the hierar-chy of quark and lepton masses. Also, within the SM, thethe flavor mixing and CP violation in weak interactionsarise from the quark-Higgs Yukawa couplings, and neu-trino masses, whatever their origin, require a coupling ofneutrinos to the Higgs field. If we wish to learn moreabout these features of the fundamental laws of nature,an obvious course is to measure the Higgs boson as wellas we are able. We will argue in this section and thesucceeding ones that ILC will be able to determine themass of the Higgs boson to a part in 10 and the majorcouplings of the Higgs boson to better than 1% accuracy.This will qualitatively sharpen the picture of the Higgs9boson that we will obtain even from the high-luminositystage of the LHC.This set of measurements, and other measurementsavailable for the first time at the ILC, will open newpaths in the search for new fundamental interactions be-yond the SM. Though the SM seems to account for allelementary particle phenomena observed up to now, it ismanifestly incomplete. It not only does not answer butactually is incapable of answering the questions posed inthe previous paragraph. It also cannot address basic factsabout the universe in the large, in particular, the excessof matter over antimatter and the origin of the cosmicdark matter. To make progress, we need observationalevidence from particle physics of violations of the SM.These will provide clues that can show the way forward.Up to now, we have sought evidence for new interac-tions from direct searches for new particles at LEP, theTevatron, and the LHC, from measurements of the W and Z bosons, and from searches for anomalies in fla-vor physics. We are now approaching the limits of thesetechniques with current particle physics facilities. TheILC will extend our search capabilities in precision mea-surements of W boson couplings and fermion pair pro-duction, and will provide new opportunites for the directdiscovery of new particles. But, most of all, it will opena completely new road through the high-precision studyof the Higgs boson. It is often said that the Higgs boson, as observed atthe LHC, is an uninteresting particle, since it conformsso well to the expectations from the SM. In fact, asidefrom our knowledge of the Higgs boson mass, the mea-surements make so far at the LHC tell us almost nothingabout the true nature of this particle. We now explainthis statement, and, in the process, clarify the require-ments for measurements of the Higgs boson couplingsthat can give insight into physics beyond the SM.New physics can correct the Higgs boson couplings inmany ways. However, in all cases, the size of the correc-tions is limited by the Decoupling Theorem, enunciatedby Haber in [117]: If the new particles that modify theSM have minimum mass M , then the corrections to theSM predictions for the Higgs boson couplings are of size a m H /M . (1)where the coefficient a is of order 1. The exclusions of newparticles through searches at the LHC suggest that M isat least close to 1 TeV. Then the effects of new physicsare limited to levels below 10%. We will illustrate thisresult with explicit models in the next subsection.The proof of the theorem is simple and illustrative.It can be shown that the SM is actually the most gen-eral renomalizable quantum field theory with SU (3) × SU (2) × U (1) gauge symmetry and the known particlecontent. If we add new particles with masses of M andabove, we can assess their influence on the Higgs boson by integrating them out of the theory. This adds to theLagrangian a set of new terms with the SM symmetries.The terms in the new Lagrangian can be organized bytheir operator dimension as L = L SM + 1 M (cid:88) i c i O i + 1 M (cid:88) j d j O j + · · · (2)where L SM is the SM Lagrangian, O i are operators of di-mension 6, O j are operators of dimension 8, etc. Shiftsin the SM parameters due to new physics are not ob-servable, since these parameters are in any case fit toexperiment. Then the leading observable corrections areof order M − .This theorem has a striking consequence. Instead ofa model with a single Higgs doublet, as we have in theSM, nature could be providing a model with two or moreHiggs fields, composite Higgs fields, even a whole Higgssector. All of this possible complexity is hidden from usby the Decoupling Theorem.The theorem has an appealing corollary, though. Sincethe SM is the most general renormalisable model, onceits parameters are known, its predictions for the Higgscouplings are determined precisely. These predictions dodepend on measured SM parameters such as m b , m c , and α s , but it is argued in Ref. [118] that lattice QCD willdetermine these well enough to fix the SM predictionsfor Higgs to part-per-mil accuracy. Then, if we can ob-serve corrections to the SM predictions at the 1% level,these corrections and the evidence that they give for newphysics cannot hide. Many models of physics beyond the SM illustrate thepoints made in the previous section. These examplespoint to a goal of 1% accuracy for the measurement ofHiggs boson couplings in the major decay modes.Models with two Higgs doublets contain 5 physicalHiggs particles: two neutral CP -even states h , H , a neu-tral CP -odd state A , and a pair of charged scalars H ± .These states are mixed by two angles α, β . The lighter CP -even state h is identified with the observed Higgsboson. Its couplings to fermions depend on the mixingangles. For example, in the “Type II” case, g ( Hbb ) = − sin α cos β m b v g ( Hcc ) = cos α sin β m c v . (3)However, the mixing angles are connected to the massesin such a way that when the additional bosons becomeheavy, their effects in (3) also become small, − sin α cos β = 1 + O ( m Z m A ) , (4)conforming to the Decoupling Theorem. In Type II mod-els, the b and τ Yukawa couplngs are shifted together by0
FIG. 22: Deviation from the SM prediction for the
Hbb coupling over a parameter space of grand-unified SUSYmodels, from [119]. Models in the upper left-hand corner areexcluded by current LHC searches. Models above the dashedline are expected to be excluded at the HL-LHC. Thecolor-code indicates the magnitude of the couplingdeviation, in %. about 5% for m A = 500 GeV, and by decreasing amountsas all of the additional bosons become heavier.Supersymmetry (SUSY) models contain Type II two-Higgs-double sectors, but they also contain other effectsthat modify the Higgs boson couplings. Mixing betweenthe scalar partners of b L and b R can generate a shift ofthe Hbb coupling through loop diagrams. The magnitudeof this effect in grand-unified SUSY models is shown inFig. 22 [119]. Note that it is possible to have a largeshift of the Higgs boson coupling for parameter values atwhich the SUSY particles are too heavy to be discoveredat the LHC. Thus, the search for shifts in the Higgs cou-plings away from the SM predictions provides a methodof searching for this new physics that is independent of,and largely orthogonal to, the direct search for SUSYparticles. Other surveys of this effect in [120, 121] con-firm this idea.SUSY models typically predict very small shifts of the
HW W and
HZZ couplings, but other types of modelscan affect these couplings directly. Models in which theelectroweak phase transition becomes first-order and al-lows baryogenesis at the weak scale often involve mixingof the Higgs field with a heavy singlet field. This gives g ( HW W ) = 2 m W v cos φ ≈ m W v (1 − φ ) , (5)where φ ∼ m H /m S , and similarly for the HZZ cou-pling [122]. In composite models of the Higgs field, theHiggs boson often appears as a Goldstone boson of a newstrong interaction theory, giving a coupling modificationby (1 − v /f ) / , where f is the Goldstone boson decayconstant [123]. This effect is similar to that in (5). Models of Higgs compositeness, “Little Higgs” models,and models with extra space dimensions all contain newheavy vectorlike fermions T . Typically, these fermionsobtain a fraction of their mass from the Higgs mechanism(perhaps by mixing with the top quark) that is of order m t /m T . Then they induce corrections of this order tothe loop-generated Higgs couplings g ( Hgg ) and g ( Hγγ ).Corrections as large as 10% can be generated in specificmodels [124]. The same mixing and compositeness effectsmodify the
Htt coupling [125].An interesting picture emerges. Almost all models ofnew physics generate corrections to the Higgs boson cou-plings. Almost always, these corrections are small, belowthe 10% level, in accord with the Decoupling Theorem.However, in precision experiments that make these cou-pling deviations visible, each type of new physics affectsthe Higgs couplings in different ways. In general, • The
Hbb and
Hτ τ couplings are sensitive to modelswith additional Higgs doublets. • The
Hbb coupling is sensitive to heavy SUSY par-ticles with left-right mixing. • The
HW W and
HZZ couplings are sensitive tomixing of the Higgs field with singlet fields, and tocomposite structure of the Higgs boson. • The
Hgg and
Hγγ are sensitive to models with newvectorlike fermions. • The
Htt coupling is sensitive to models with com-posite Higgs bosons and top quarks.In each new physics model, the deviations from theSM predictions for the Higgs couplings form a pattern.With precision experiments, it is possible not only todiscover the existence of new physics but also to readthe pattern and gain clues as to the way forward. Aworked example of such model discrimination at the levelof precision expected at the ILC is presented in Section 7of Ref. [3].
Today, the LHC experiments are achieving 20% un-certainties in their measurements of Higgs boson cou-plings. Over the lifetime of the LHC, including its high-luminosity stage, these experiments will acquire a factorof 30 more data. Shouldn’t this lead to Higgs couplingmeasurements of the required high precision? We believethat the answer to this question is no. We give a high-level argument here. A detailed comparison of the ex-pected ILC capabilities with those of the high-luminosityLHC will be presented in Sec. 11.3.We find three points relevant to this comparison. First,the measurement of Higgs boson decays at the LHC isextremely challenging because of the difficulty of distin-guishing signal from background. In the two decay modesin which the Higgs boson was discovered, H → γγ and1 H → (cid:96) , Higgs events are apparent, because all productsof the Higgs are observed and the Higgs mass can bereconstructed with high accuracy. Unfortunately, thesemodes correspond to tiny branching ratios, 0.2% and0.02% of Higgs decays, respectively. For more typicaldecay modes, Higgs boson decay events have no obviousdifferences in appearance from SM background reactionswith larger rates. For example, H → W W → eνµν events differ from qq → W W → eνµν events only insubtle features of the final state. To discover the Higgsboson in one of the major channels, the LHC experimentsstart from samples that are 10:1 background to signal inthe highest significance regions. (For H → bb , the ratiois 20:1.) They then extract the signal by multivariateanalysis and the use of machine-learning classifiers. It isalready a triumph that ATLAS and CMS have been ableto obtain significant observations.Measuring the Higgs couplings with high precision iseven more of a challenge. It is currently beyond the stateof the art to determine the efficiency for the rejectionof SM background events from these signal regions to1% accuracy. The residual background events must besubtracted from the Higgs signal, and so this 1% wouldtranslate to a 10% accuracy on the Higgs σ × BR or a5% error on the coupling. To go beyond this level istruly daunting. Nevertheless, the studies reported in theHL-LHC Yellow Book [126] demonstrate that the HL-LHC can be expected to push beyond this level and reachaccuracies on Higgs boson couplings of 2–4%.This brings us to the second point. As we have em-phasized already, the modifications of the Higgs bosoncouplings from new physics are expected to be small. Inthe previous section, we have argued that new physics in-teractions typically affect specific Higgs boson couplingsat a level of 5% or smaller. A 2% measurement of such acoupling would not meet even the 3 σ criterion for positiveevidence of new physics.Finally, one must take into account that the HL-LHCmeasurements will ultimately be limited by the system-atic understanding of backgrounds. Any deviation inHiggs couplings observed at the LHC is likely to be ques-tioned (as, for example, the tt forward-backward asym-metry from the Tevatron was) without a clear means ofconfirming the result. One sometimes hears that the LHCcan measure ratios of branching ratios with improved ac-curacy, but this statement is not borne out by resultspresented in Ref. [126], since each mode has differentbackgrounds and requires its own dedicated analysis.In contrast, as we will argue below, the observation ofHiggs coupling deviations at the ILC at 250 GeV will bevery robust. It will be be statistics-limited, and it canbe confirmed by experiments at 500 GeV that bring in anew production reaction with an independent data set. e + e − → ZH The arguments just presented call out for a differentway to measure Higgs boson couplings. In this method,Higgs boson events should be apparent with a simple
FIG. 23: Event displays of e + e − → ZH events with Z → µ + µ − , from full simulation: Left: H → τ + τ − , ILDdetector model; Right: H → bb , SiD detector model. discriminator that can then be refined for high-accuracy σ × BR measurements. Ideally, this method should iden-tify Higgs boson events independently of the decay mode,allowing the measurement of the total cross section forHiggs production and the discovery of exotic and unan-ticipated Higgs decays.This new method will be provided by the ILC. It is themeasurement of the reaction e + e − → ZH at 250 GeV.At an e + e − collider at this energy, it is true to a first ap-proximation that any Z boson observed with a lab energyof 110 GeV is recoiling against a Higgs boson. The back-grounds to this signature (present at about 30% of thesignal level before cuts) come from radiative e + e − → Zγ and e + e − → ZZ , reactions that are well-understood andcomputed from electroweak theory at the 0.1% level.The reaction e + e − → ZH provides tagged Higgs de-cays. Thus, events can be selected independently of theHiggs decay mode. Then (1) the total cross section forthis reaction can be measured, giving a means of ab-solutely normalizing Higgs boson couplings; (2) Higgsbranching ratios can be measured by counting, indepen-dently of the production cross section; and, (3) exotic de-cay modes of the Higgs boson can be observed as productsrecoiling against the Z tag. Some event displays, fromfull simulation, are shown in Fig. 23. The fact that the reaction e + e − → ZH yields tagged Higgs decays opens the possibility of another type ofsearch for new physics. The Higgs field is unique amongSM fields in that it can form a dimension-2 operator Φ † Φwith zero SM quantum numbers. If there is any sectorof fields that contains its own scalar field Σ, there will ingeneral be a renormalizable coupling∆ L = η (Φ † Φ) (Σ † Σ) . (6)The coupling constant η is dimensionless, so the connec-tion can be made at any (high) mass scale. Thus it ispossible for the Higgs boson to access a sector of elemen-tary particles that have no other connection to the fieldsof the SM.2If there is a new sector of particles with zero SM quan-tum numbers such that some of those particles have pair-production thresholds below 125 GeV, those particlesshould appear in Higgs boson decays. If the particle thatmakes up cosmic dark matter is light enough to be pro-duced in this way, the Higgs boson will have decays toinvisible final states. It is also possible that the newparticles are unstable with respect to decay back to SMmodels. Such decays could produce a number of differentexotic final states, including 4 b , 4 τ , bb + invisible states,and new particles with long lifetimes [127]. With the datasample of the 250 GeV ILC, it is possible to search forall of these decay modes. For invisible Higgs decays, theexpected 95% CL exclusion limit on the branching ratiois 3 × − , and for visible or partially visible modes thelimits are in the range 10 − –10 − [128]. Though the goals of measuring the SM and exoticbranching ratios of the Higgs boson are already very im-portant, experiments at the ILC allow a further step.The theory predictions described in Sec. 4.2 refer to ab-solute partial decay widths. These are related to theHiggs branching ratios byΓ( H → AA ) = Γ tot · BR ( H → AA ) . (7)The Higgs boson total width is very small—4 MeV inthe SM—and it is not expected that any proposed col-lider can measure this value directly with percent-levelprecision. However, as we will now show, the ILC candetermine the total width of the Higgs in a way that ishighly model-independent and allows a 1% absolute nor-malization of Higgs coupling constants.A possible method to determine the Higgs width is tomultiply each HAA coupling by a parameter κ A , andthen fit these prarameters using data from e + e − → ZH .In this simple method, the total cross section for e + e − → ZH is proportional to κ Z and so the κ A parameters canbe absolutely normalized. This method has been used inmuch of the literature on Higgs coupling determinations,including [129]. In that paper, invisible and visible butexotic decay modes were treated by including these twopartial widths as two additional parameters in the fit.Using as inputs the measureable σ × BR s for SM Higgsdecay channels and Higgs decays to invisible final states,plus the total cross section for e + e − → ZH , the ILC datawould give a well-defined fit to the κ A parameters.There are two problems with this method. First, themethod is not completely model-independent. Modellingthe effects of new physics as a general set of dimension-6operators as in (2), we find two different Lorentz struc-tures for the modifications of the HZZ vertex,∆ L = (1 + η Z ) m Z v hZ µ Z µ + ζ Z v hZ µν Z µν , (8)where Z µ is the gauge field and Z µν is the field strength,and a similar pair of structures for the HW W vertex. The ζ V coefficients have interesting phenomenologicalsignificance. In weakly coupled models such as super-symmetry, these couplings are generated only by loopdiagrams and have very small values; however, in com-posite Higgs models these coefficients can be comparableto the η V coefficients. This makes it important to be ableto determine the two couplings independently determinedfrom data. The second problem with the method givenin the previous paragraph is that it does not make themost effective use of the data set from e + e − colliders.The total width of the Higgs boson is determined fromthe ratio σ ( e + e − → ZH ) / Γ( H → ZZ ∗ ). Since branch-ing ratio for H → ZZ ∗ is only 3%, this strategy sacrificesa factor 30 in statistics.A much more effective method for fitting Higgs bo-son couplings is described in [3]. In this method, wemodel the effects of new physics by the most general setof dimension-6 operators that can appear in (2). Thecomplete set of SU (3) × SU (2) × U (1)-invariant lepton-and baryon-number conserving dimension-6 operators in-cludes 59 terms [130]. However, for the analysis of e + e − collider data, we can restrict ourselves to electron reac-tions producing the Higgs boson and other color-singletstates. Since there is a single SM effective Lagrangianthat should apply to all processes, this method allowsus to combine data on Higgs production with additionaldata sets from e + e − → W + W − and precision elec-troweak measurements. It is also possible to make useof additional observables for Higgs production beyondsimple rates. In particular, the angular distribution andpolarization asymmetry in e + e − → ZH play importantroles. These considerations give the method based onEffective Field Theory much more power in extractingthe most accurate estimates of the Higgs boson couplingsfrom the data.It is sometimes considered a restriction that the EFTmodel contains only operators of dimension 6 withoutconsidering operators of dimension 8 and higher. How-ever, there is a useful analogy to precision electroweakmeasurements. There, the effects of the top quark andthe Higgs boson are well-modeled by the S and T param-eters [131]—which are part of the dimension-6 effectivefield theory description—even though the masses of theseparticles are not far above the Z mass. Only when newparticles are discovered and one wishes to compute theireffects in detail is it necessary to go beyond the leadingcorrections. Very light new particles can have a differenteffect that is not accounted for by Effective Field The-ory, since they can provide new Higgs decay channelsthat give additional contributions to the Higgs width.We take these possible effects into account explicitly asadditional parameters in our global fit, as we will explainin Sec. 11.1.After we describe the experimental methods and theexpected measurement uncertainties for Higgs produc-tion in Sec. 8 and for W pair production in Sec. 9, wewill present formal projections for uncertainties in Higgscouplings in Sec.11, making use of the EFT method.3 FIG. 24: Feynman diagrams contributing to the process e + e − → W + W − when contributing dimension-6 operatorsare included. We will show that the data set expected for the ILCat 250 GeV will measure the
Hbb couplings to 1% ac-curacy, the
HW W and
HZZ couplings to better than0.7%, and the other major SM Higgs couplings to ac-curacies close to 1%. These measurements should bestatistics-limited. Above 250 GeV, a second Higgs pro-duction reaction, e + e − → ννh through W boson fusionbecomes important. We will show that, using the addi-tional data on e + e − → ZH and the independent mea-surements from the W fusion reaction, the uncertaintieson Higgs couplings will decrease by another factor of 2. e + e − → W + W − The reaction e + e − → W + W − contributes to the anal-ysis described above, but it has its own independent in-terest. This reaction provides an excellent way to test forthe presence of dimension-6 operators that involve the W and Z fields. The Feynman diagrams contributing to thereaction are shown in Fig. 24. The process involves in-terference between s -channel diagrams with γ and Z ex-changes and a t -channel diagram with neutrino exchange.In the SM, there are large cancellations among these di-agrams, but these are not respected by the dimension-6contributions. Thus, the dimension-6 coefficients appearin the cross section formula enhanced by a factor s/m W .The largest part of the dimension-6 effect can be de-scribed by shifts of the form factors for the W W γ and
W W Z vertices. These vertices can be parametrized as[132]∆ L = ig V (cid:26) V µ (cid:0) ˆ W − µν W + ν − ˆ W + µν W − ν (cid:1) + κ V W + µ W − ν ˆ V µν + λ V m W ˆ W − µ ρ ˆ W + ρν ˆ V µν (cid:27) , (9)where V = A or Z . In the SM, g A = e , g Z = es w /c w and the other coeficients are zero at the tree level. The re-sult g A = e is exact due to the QED Ward identity. Thedimension-6 operator corrections generate a 3-parametershift of the other 5 coefficients. These shifts can in prin-ciple be measured both at electron and at hadron collid-ers. However, measurements in e + e − have definite ad-vantages. First, it is possible to use final states withhadronic W decays to determine the complete kinemat-ics of each event and, using this information, to separate the production of transverse and longitudinal W bosons.Then, using beam polarization and W final-state polar-ization, the 3 possible shifts of the form factors can bemeasured separately. Second, the greater intrinsic accu-racy of measurements in e + e − give excellent results ata center of mass energies of 250–500 GeV. At hadroncolliders, the factor s/m W can be much larger, and onecan take advantage of this by observing the reaction at W W pair masses above 1 TeV. However, this can lead toambiguities due to the possible influence of dimension-8operators, whose effects grow as ( s/m W ) [133].In Sec. 9 below, after describing the experimental studyof e + e − → W + W − , we will show that the ILC at250 GeV is expected to improve the precision of W formfactor measurements by an order of magnitude over ex-pected results from the HL-LHC. e + e − → f f Fermion pair production provides a search for newforces that couple directly to the electron. At LEP andLHC, e + e − and qq annihilation are used as probes fornew gauge bosons appearing in the s -channel and for sig-nals of fermion compositeness.The comparison with LEP 2 is instructive. The ILCwill operate at an energy not so far above that of LEP 2(250 GeV vs. − vs. a total of 1 fb − over 4 experiments).For statistics-limited measurements, this gives a factor (cid:20) s · (cid:82) L| ILC s · (cid:82) L| LEP (cid:21) / ≈
60 (10)improvement in sensitivity to deviations from the SM,or an improvement of 7.5 in the mass scale that can beaccessed. Though the comparison depends on the par-ticular model, this corresponds to the ability to observednew vector bosons at 5–6 TeV and contact interactionscales of 70 TeV, comparable to the projected reach ofthe HL-LHC.In addition, the information from ILC is very specific.Measuring the cross section for e + e − → f f in the for-ward and backward directions for e − L and e − R beams givesfour different observables, each of which corresponds toa different dimension-6 effective interaction. Discoveryof an anomaly points directly to a model interpretation,either with an s -channel resonance or with new inter-actions at higher energy. This information can be puttogether with results of resonance searches at the LHC.The reaction e + e − → bb deserves special considera-tion. In models in which the Higgs boson is composite,typically either the t L or the t R must be composite alsoto generate a large enough t quark mass. The b L is the SU (2) partner of the t L and so must have the same ad-mixture of composite structure. If it is the t R that ismore composite, it is not required that the b R is compos-ite, but this often happens in models. This can generatefew-percent corrections to the rates for e − L,R e + → b R b L at the ILC [134, 135]. It is possible that this effect, rather4than effects in Higgs decays, would be the first indicationof a composite Higgs sector. Despite the wide range of direct searches for new par-ticle pair production at the LHC, those searches haveblind spots corresponding to physically interesting mod-els. The two most important of these are:1. Insensitivity to new particles with electroweak in-teractions only that decay to an invisible partnerwith a mass gap of less than 5 GeV. Though thiscase seems quite special, this is exactly the setof properties predicted for the charged Higgsinoof SUSY models. Dark matter scenarios involv-ing coannihilation can also fall into this blind spot,since in those models there is an electroweak part-ner separated from the dark matter particle by k B T at the thermal dark matter freezeout temperatureof 5-10 GeV.2. Insensitivity to production of pairs of invisible par-ticles observed through radiation of an initial-stategluon. At the LHC, such “mono-gluon” events haveas a background initial state radiation in the Drell-Yan process, and the sensitivity to such events islimited by the precision of our knowledge of theDrell-Yan cross section.In both cases, the ILC can detect these new physicsevents for particle masses almost up to half of the col-lider center of mass energy.The experimental aspects of these particle seaches arediscussed in Sec. 12. A broader review of the opportu-nities for new particle discovery at e + e − colliders can befound in [136]. One theme that runs through all of the analyses dis-cussed in the following sections is the important role ofbeam polarisation. The use of beam polarisation maybe unfamiliar to many readers, since all recently oper-ated colliders – the Tevatron, PEP-II and KEKB, andthe LHC – have had unpolarised beams. In hadroniccollisions, the effects of polarisation are relatively small,first, because the dominant QCD interactions conserveparity and, second, because the proton is a compositeparticle, so high proton polarisation translates to muchsmaller polarisation for the constitutent quarks and glu-ons. At a high-energy e + e − collider, the situation is verydifferent. The dominant interaction is the electroweakinteraction, which has order-1 parity asymmetries in itscouplings. The beam particles are elementary, so that80% beam polarisation translates to 80% polarisation inthe colliding partons. This implies that polarisation ef-fects are large at e + e − colliders and can be used to greatadvantage. It is very challenging to achieve high beam polarisationin circular colliders, especially for longitudinal polarisa-tion. Transverse beam polarisation was observed at LEPin single- and separated-beam operation but not for col-liding beams [137]. However, a linear electron or positroncollider naturally preserves longitudinal beam polarisa-tion. The design of the ILC has been thought throughto produce, maintain, and control beam polarisation forboth electrons and positrons, as has been explained inSec. 2.3.1. This brings advantages for physics that wenow discuss.There are three major uses of beam polarisation in theexperiments planned for ILC:1. Measurement of helicity-dependent electroweakcouplings.2. Suppression of backgrounds and enhancement ofsignals.3. Control of systematic uncertainties.We discuss the first two of these points here. The third,which is particularly important to claim a discovery fromprecision measurements, is discussed in Sec. 8.3. A com-prehensive review of the role of polarisation with manymore examples can be found in [116], and, for positronpolarisation in particular, in [110].To begin, we need some notation. Let P e − and P e + be,respectively, the longitudinal polarisations of the electronand positron colliding beams, equal to +1 for completelypolarised right-handed beams and − σ RR , σ RL , σ LR , σ LL bethe cross sections for a given process with completely po-larised beams of the four possible orientations. Since theelectron has only two spin states, the cross section forgeneral beam polarisations is given by σ P e − P e + = 14 (cid:8) (1 + P e − )(1 + P e + ) σ RR +(1 − P e − )(1 − P e + ) σ LL +(1 + P e − )(1 − P e + ) σ RL +(1 − P e − )(1 + P e + ) σ LR (cid:9) , (11)For s -channel e + e − annihilation processes, helicityconservation implies that only σ RL and σ LR are nonzero.In this case Eq. (11) reduces to the simpler form σ P e − P e + = 2 σ ( L eff / L ) [1 − A LR P eff ] (12)where σ is the unpolarised cross section, and L eff and P eff are the effective luminosity and polarisation, defined,respectively, as P eff = P e − − P e + − P e + P e − and L eff = 12 (1 − P e + P e − ) L . (13)The coefficient A LR is the intrinsic left-right asymmetryof the reaction cross section, A LR = σ LR − σ RL σ LR + σ RL . (14)5In the electroweak interactions, it is typical that left-handed fermions have larger coupling constants thanright-handed fermions. Then, choosing P e − to be left-handed (negative) and P e + to be right-handed (positive)can confer important advantages. Consider, for example,the typical ILC values P e − = − P e + = +30%. Thenthe effective polarization Eq. (13) for the measurementof A LR values is P eff = 90%. The Higgsstrahlung processhas a rather small polarisation asymmetry, A LR = 0 . • In e + e − → f f , the e − L and e − R couple to differentlinear combinations of the s -channel γ and Z prop-agators. Beam polarisation allows us to measurethe couplings to these vector bosons independently.In addition, an s -dependent change in the polari-sation asymmetry can signal the presence of a new s -channel resonance. • Similarly, in e + e − → W + W − , the separation of γ and Z couplings can be combined with informa-tion from the W production angle and polarisationsto completely disentangle the 14 complex parame-ters (28 real parameters) in the most general La-grangian for triple gauge vertices. • In e + e − → ZH , measurement of the polarisationasymmetry plays an important role in disentanglingthe various of parameters that enter the EFT anal-ysis of Higgs boson couplings. • If new particles are discovered in pair-productionat the ILC, measurement of the production crosssection with different beam polarisation settings al-lows their electroweak quantum numbers to be de-termined unambiguously.We will illustrate all of these points in the sections tofollow.It is also possible to take advantage of differences in thepolarisation effects on signal and background cross sec-tions to enhance signals and control backgrounds. Unlikeannihilation processes, radiative Bhabha scattering and2-photon processes have nonzero σ LL and σ RR , so it ispossible to test strategies for the suppression of thesebackgrounds using data sets with in which P e − and P e + have the same sign. The reaction e + e − → W + W − hasa relatively large cross section among annihilation pro-cesses and is often the dominant background to studies ofor searches for other processes. However, this process alsohas a large polarisation asymmetry, with σ LR /σ RL ≈ P e − = +80%, P e + = −
30% essen-tially turns off this background.As an example of the effectiveness of background sup-pression, we show in Fig. 25 a comparison of searchesfor invisible dark matter particles χ in the mono-photon [GeV] c M
50 100 150 200 250 [ G e V ] L EFT not validILDVector, 500GeV
Only stat. uncertainties) = (+80%,-30%) + ,e _ , P(e -1 -1 + ,e _ , P(e -1 -1 e xc l u s i on r eg i one x pe c t ed W I M P FIG. 25: Comparison of the 95% confidence lower limit onthe mediator scale for dark matter production using themono-photon channel, for different assumptions onluminosity and polarisation. See Sec. 12 for a description ofthe analysis [106]. Note that this plot considers statisticaluncertainties only . The corresponding comparison includingsystematic uncertainties is shown in Fig. 59. mode e + e − → γ + χχ under different assumptions onluminosity and polarisation. The predicted 95% confi-dence lower limit on the mediator scale Λ is shown asa function of the χ mass. The expected limit for an un-polarized collider is shown as the black solid curve. Forthis analysis, the statistically optimal choice is that of(+80% , − e.g. , Higgs measurements) that might be done inthe same run. But the figure also shows that a data setof 1.6 ab − with optimal polarisation is considerablymore powerful than a data set of 4 ab − with unpo-larised beams. The red dotted curve shows the result forthe H20 scenario with polarisations given in Tab. V. Forclarity, the figure includes statistical errors only.The influence of polarisation on systematic errors isequally important. Where experiments with unpolarisedbeams give one measurement, experiments with bothelectron and positron beams polarised give 4 independentmeasurements. These can be used as cross-checks for theunderstanding of systematics, and also to form combi-nations in which the dominant systematic errors cancel.We will discuss this point in more detail in Sec. 8.3.
5. PHYSICS CASE –BEYOND 250GEV
A key advantage of linear colliders is the possibilityto upgrade the center-of-mass energy. The energy reachof circular electron-positron colliders of a given circum-ference is limited by synchrotron radiation, and this is6difficult to overcome because of the steep growth of syn-chrotron losses with energy. Linear colliders, however,can be upgraded to reach higher center of mass energieseither by increasing the length of the main linacs or byinstalling linac components that support higher acceler-ating gradients.In the major particle physics laboratories, the lifetimeof collider elements and infrastructure has rarely beenlimited to the scope of the project they were designed andbuilt for. A famous example is the Proton Synchrotronat CERN. Initially commissioned in 1959, it is still in op-eration as part of the accelerator complex that preparesprotons for injection in the Large Hadron Collider. Inthis accelerator complex, the expensive civil engineeringefforts to construct each component are reused, so thattheir cost is effectively shared. The tunnel that was con-structed for LEP now hosts the Large Hadron Colliderand its luminosity upgrade. In very much the same way,we expect that the ILC will form the seed for a facilitythat contributes to the cutting edge of particle physicsfor decades. For electron-positron collisions, any facilityat energies much higher than those already realised mustbe a linear collider in a long, straight tunnel. The ILCnaturally offers a setting for this program.The ILC project today would be an e + e − colllider of250 GeV in the center of mass. But, already, considerablethought and planning has already gone into the exten-sion of this machine to higher energies. In this section,we will briefly describe the further physics opportunitiesthat the ILC will offer at 350 GeV, 500 GeV, and be-yond. The physics goals for higher-energy e + e − collidershas already been discussed extensively in the literature.Particularly useful references are the volumes presentingdetailed studies carried out for the ILC [129, 138] andCLIC [139–141] design reports. As explained in Sec. 2.4.1, the ILC TDR includes pro-visions for running of the ILC at 500 GeV and 1 TeV.The most obvious energy upgrade path is an extensionof the linear accelerator sections of the colliders, whichprovides an increase in center-of-mass energy that is pro-portional to the length of the linacs. The design of theILC presented in the TDR [1, 14, 15] envisaged a center-of-mass energy of 500 GeV in a facility with a total lengthof 31 km. The ILC TDR also documents a possible ex-tension to 1 TeV based on current superconducting RFtechnology. Space for a tunnel of 50 km length is avail-able at the Kitakami site in Japan, enough to accomodatea 1 TeV machine based on the TDR technology.An even larger increase in center-of-mass energy maybe achieved by exploiting advances in accelerator technol-ogy. The development of cavities with higher accelerat-ing gradient can drive a significant increase in the energywhile maintaining a compact infrastructure. Supercon-ducting RF technology is evolving rapidly. Importantprogress has been made toward developing cavities witha gradient well beyond the 35 MV/m required for the ILC [35, 41] and even beyond the 45 MV/m envisagedfor the 1 Tev ILC. In the longer term, alternate-shapeor thin-film-coated Nb Sn cavities or multi-layer coatedcavities offer the potential of significantly increased cav-ity performance [14]. Novel acceleration schemes mayachieve even higher gradients. The CLIC drive beamconcept has achieved accelerating gradients of up to 100MV/m [142]. Finally, the advent of acceleration schemesbased on plasma wakefield acceleration or another ad-vanced concept could open up the energy regime up to30 TeV. A report of the status of accelerator R&D andremaining challenges is found in Refs. [143, 144], withfurther details and a brief description of the potential ofsuch a machine in the addendum [145].Thus, the ILC laboratory has paths to evolve into alaboratory for electron-positron collisions at higher ener-gies, and possibly even to a laboratory that can offer thehighest parton-parton center of mass energies achievableat any collider.
Operation of the ILC at higher energies will producenew data sets that will substantially improve the capa-bilites of the ILC for all of the physics topics presentedin Sec. 4. The ILC simulation studies included extensivestudies at 500 GeV and also studies at 1 TeV in the cen-ter of mass. We will present the results of these studiestogether with our studies from 250 GeV in the followingsections.Data-taking at higher energies will improve the resultsfrom 250 GeV and give access to new SM reactions. Letus first summarize the expected improvements in the ar-eas that we have discussed so far: • For Higgs production, running at 500 GeV will adda new data set of e + e − → ZH events. It willalso provide a substantial data set of e + e − → ννH events, corresponding to W W fusion production ofthe Higgs boson. With these new samples, it willbe possible to confirm any anomalies in the Higgsboson coupling seen at 250 GeV and to providean independent comparison of the ZZ and W W couplings. Though the backgrounds to the Higgsproduction processes are relatively small for bothreactions, they are different in the two cases, pro-viding a nontrivial check of some systematics. Inglobal analysis, as we will see in Sec. 11, the ad-dition of 500 GeV data leads to a decrease in theuncertainties on Higgs boson couplings by about afactor of 2 and a decrease in the uncertainty on theHiggs total width by a factor 1.6. • For
W W production, running at 500 GeV will givea data set of roughly the same size as that obtainedat 250 GeV. Further, since the effects of anomalous W couplings, or the corresponding dimension-6 op-erators, increase as s/m W , the new data set will7provide much more sensitive constraints on theireffects. • For f f production, similarly, the possible new ef-fects due to heavy gauge bosons or contact interac-tions scale as s/M , where M is the new mass scale.The discovery potential for M , or new limits, willincrease by a factor close to 2. • For new particle searches, the reach in e + e − pairproduction is close to half the e + e − centre-of-massenergy. The improvement in reach is particularlyrelevant for color-singlet particles such as heavyHiggs bosons, electroweakinos, Higgsinos, and darkmatter particles.All of these observations illustrate the more generalpoint that higher energy can be an important tool intests of the SM using Effective Field Theory. We haveemphasized that an analysis within EFT allows a moreincisive search for new physics effects on Higgs bosoncouplings by bringing together a large number of observ-ables from different physical processes. In the EFT for-mulae, the various operator contributions have differentenergy-dependence, with certain operators having an im-pact that grows strongly with energy. Thus there is greatadvantage in combining a data set taken at 250 GeV withone or more data sets taken at higher energies. Beyond the improvement in areas that we have alreadydiscussed, the operation of the ILC above 250 GeV cangive access to new and important SM reactions. AmongHiggs boson couplings, there are two that are inaccessibleat 250 GeV. These are the top quark Yukawa couplingand the Higgs boson self-coupling. In Secs. 8.5 and 10.5,we will describe the measurement of these couplings atthe ILC at 500 GeV and above. Since these couplingscan show large deviations from the SM expectation incertain classes of new physics models, it is necessary tomeasure these couplings accurately to complete the fullpicture of the Higgs boson interactions.The interest in the top quark Yukawa coupling is ob-vious. The top quark is the heaviest SM particle, and,within the SM, its mass is proportional to this couplingconstant. If there are new interactions that promote thelarge value of the top quark mass, the Yukawa couplingwill receive corrections, and so it is important to probefor them.The measurement of the trilinear Higgs coupling is anequally important goal of a complete program of studyfor the Higgs boson. While the measurement of the Higgsfield vacuum expectation value and the mass of the Higgsboson express the mass scale of the Higgs field potentialenergy and its variation, the trilinear Higgs coupling givesinformation on the shape of the potential energy functionand brings us closer to understanding its origin.The trilinear Higgs coupling is sensitive to the natureof the phase transition in the early universe that led to the present state of broken electroweak symmetry. TheSM predicts a continuous phase transition. This hasimplications for models of the creation of the matter-antimatter asymmetry that we observe in the unversetoday. According to Sakharov’s classic analysis [146], thenet baryon number of the universe needed to be createdin an epoch with substantial deviations from thermalequilibrium in which CP - and baryon-number-violatinginteractions were active. The baryon number of the uni-verse could have been created at the electroweak phasetransition, making use of new CP -violating interactionsin the Higgs sector, but only if the phase transition wasstrongly first-order. In explicit models, this typically re-quires large deviations of this coupling, by a factor 1.5–3,from its SM value [147]. e + e − reactions In addition, the extension of the ILC to higher energieswill allow the precision study of the top quark. This isan essential goal of precision experiments on the SM, fortwo reasons. First, similarly to the Higgs boson, the topquark stands closer to the essential mysteries of the SMthan any other quark or lepton. It is heavier than thenext lighter fermion, the b quark, by a factor of 40 andheavier than the lightest quark, the u quark, by a factorof 10 . The reasons for this are unknown, but they mustbe related to other mysteries of the Higgs sector and SMmass generation. In fact, it is not understood whether thetop quark is a “heavy” quark because of special interac-tions that the other quarks do not share or, alternatively,whether the top quark is an “ordinary” quark receivingan order-1 mass while the masses of the other quarks arehighly suppressed. Competing extensions of the SM suchas supersymmetry and composite Higgs models differ intheir answers to this question.Second, the fact that the top quark has spin, couplesto the parity-violating weak interactions, and decays tononzero spin particles through t → bW gives a largenumber of independent observables for each tt produc-tion process. An e + e − collider with beam polarizationcan take advantage of all of these observables, especiallyif it can produce tt well above threshold at 500 GeV inthe center of mass.Thus, top quark physics is a place in which we expectto find deviations from the predictions of the SM, in asetting where we have many handles to search for thesenew physics effects. The top quark physics potential ofthe ILC is discussed in Section 10. The energy upgrade of the ILC greatly significantly ex-tends the reach of direct searches for signatures of exten-sions of the Standard Model. Searches for new particlesat the ILC provide robust, loophole-free discovery poten-tial. Once a significant signal is observed the propertiesand interactions of the new particle can be characterized8with excellent precision. The discovery reach for mas-sive particles is primarily limited by the kinematics ofthe process, with mass limits for pair-produced particlestypically reaching half the center of mass energy. An en-ergy upgrade to 500 GeV or 1 TeV therefore yields animmediate extension of the mass reach.The possibility of an energy upgrade renders a linearcollider facility a very flexible tool, allowing it to reactto new discoveries at the LHC, at the ILC or elsewhere.The potential of the higher-energy stages for searches isevaluated in more detail in Section 12.In the following sections, we will present the capabili-ties of the ILC in all of these areas. Our discussion willbe based on explicit simulation studies using the acceler-ator properties and run plan described in Secs. 2 and 3and the detector models to be presented in Sec. 6.
6. DETECTORS
The ILC accelerator is planned with one interactionregion, equipped with two experiments. The two ex-periments are swapped into the Interaction Point withinthe so-called “push-pull” scheme. The experiments havebeen designed to allow fast move-in and move-out fromthe interaction region, on a timescale of a few hours toa day. In 2008 a call for letters of intent was issued tothe community. Following a detailed review by an inter-national detector advisory group, two experiments wereselected in 2009 and invited to prepare more detailedproposals. These are the SiD detector and the ILD de-tector described in this section. Both prepared detailedand costed proposals which were scrutinised by the in-ternational advisory group and included in the 2012 ILCTechnical Design Report [5]. In this section the two pro-posals are briefly introduced.The ILC detectors are designed to make precision mea-surements on the Higgs boson, W , Z , t , and other par-ticles. They are able to meet the requirements for suchmeasurements, first, because the experimental conditionsare naturally very much more benign than those at theLHC, and second, because the detector collaborationshave developed technologies specifically to take advan-tage of these more forgiving conditions.An e + e − collider gives much lower collision rates andevents of much lower complexity than a hadron collider,and detectors can be adapted to take advantage of this.The radiation levels at the ILC will be modest comparedwith the LHC, except for the special forward calorimtersvery close to the beamline, where radiation exposure willbe an issue. This allows the consideration of a widerange of materials and technologies for the tracking andcalorimeter systems. The generally low radiation levelsallow the innermost vertex detector elements to be lo-cated at very small radii, significantly enhancing the effi-ciency for short-lived particle identification. More gener-ally, the relatively benign ILC experiment environment permits the design of tracking detectors with minimalmaterial budget (see Sec. 7.3). This allows the detec-tors to meet the stringent requirement on the track mo-mentum resolution which is driven by the need to pre-cisely reconstruct the Z mass in the Higgs recoil analysis.This requirement translates into a momentum resolutionnearly an order of magnitude better than achieved in theLHC experiments.At the same time, although they are studying elec-troweak particle production, it is essential that the ILCdetectors have excellent performance for jets. At an e + e − collider, W and Z bosons are readily observed in theirhadronic decay modes, and the study of these modesplays a major role in most analyses. To meet the require-ments of precision measurements, the ILC detectors areoptimized from the beginning to enable jet reconstruc-tion and measurement using the particle-flow algorithm(PFA). This drives the goal of 3% jet mass resolution atenergies above 100 GeV , a resolution about twice asgood as has been achieved in the LHC experiments.Finally, while the LHC detectors depend crucially onmulti-level triggers that filter out only a small fraction ofevents for analysis, the rate of interactions at the ILC issufficiently low to allow running without a trigger. TheILC accelerator design is based on trains of electron andpositron bunches, with a repetition rate of 5 Hz, and with1312 bunches (and bunch collisions) per train (see Sec. 2,Tab. I). The 199 ms interval between bunch trains pro-vides ample time for a full readout of data from the previ-ous train. While there are background processes arisingfrom beam-beam interactions, the detector occupanciesarising from these have been shown to be manageable.The combination of extremely precise tracking, excel-lent jet mass resolution, and triggerless running gives theILC, at 250 GeV and at higher energies, a superb poten-tial for discovery.To meet these goals an ambitious R&D program hasbeen pursued throughout the past 10 years or so to de-velop and demonstrate the needed technologies. Theresults of this program are described in some detail inRef. [148]. The two experiments proposed for the ILC,SiD and ILD, utilise and rely on the results from theseR&D efforts.Since the goals of SiD and ILD in terms of materialbudget, tracking performance, heavy-flavor tagging, andjet mass resolution are very demanding, we feel it impor-tant to provide information about the level of detailedinput that enters our performance estimates. These arebest discussed together with the event reconstruction andanalysis framework that we will present in Sec. 7. In thatsection, we will present estimates of detector performanceas illustrations at the successive stages of event analysis. The SiD detector is a general-purpose experiment de-signed to perform precision measurements at the ILC. Itsatisfies the challenging detector requirements resultingfrom the full range of ILC physics processes. SiD is based9
FIG. 26: The SiD detector concept. on the paradigm of particle flow, an algorithm by whichthe reconstruction of both charged and neutral particlesis accomplished by an optimised combination of trackingand calorimetry. The net result is a significantly moreprecise jet energy measurement which results in a di-jetmass resolution good enough to distinguish between W sand Z s. The SiD detector (Fig. 26) is a compact detec-tor based on a powerful silicon pixel vertex detector, sil-icon tracking, silicon-tungsten electromagnetic calorime-try, and highly segmented hadronic calorimetry. SiD alsoincorporates a high-field solenoid, iron flux return, anda muon identification system. The use of silicon sensorsin the vertex, tracking, and calorimetry enables a uniqueintegrated tracking system ideally suited to particle flow.The choice of silicon detectors for tracking and ver-texing ensures that SiD is robust with respect to beambackgrounds or beam loss, provides superior charged par-ticle momentum resolution, and eliminates out-of-timetracks and backgrounds. The main tracking detector andcalorimeters are live only during a single bunch crossing,so beam-related backgrounds and low-pT backgroundsfrom γγ processes will be reduced to the minimum possi-ble levels. The SiD calorimetry is optimised for excellentjet energy measurement using the particle flow technique.The complete tracking and calorimeter systems are con-tained within a superconducting solenoid, which has a5 T field strength, enabling the overall compact design.The coil is located within a layered iron structure that re-turns the magnetic flux and is instrumented to allow theidentification of muons. All aspects of SiD are the resultof intensive and leading-edge research aimed at achievingperformance at unprecedented levels. At the same time,the design represents a balance between cost and physicsperformance. The key parameters of the SiD design arelisted in Table IX. The tracking system (Fig. 27) is a key element of theSiD detector concept. The particle flow algorithm re-quires excellent tracking with superb efficiency and two-particle separation. The requirements for precision mea-
TABLE IX: Key parameters of the baseline SiDdesign. (Alldimension are given in cm).SiDBarrel Technology In rad Out rad z extentVtx detector Silicon pixels 1.4 6.0 ± . ± . ± . ± . ± . ± . surements, in particular in the Higgs sector, place highdemands on the momentum resolution at the level of δ (1 /p T ) ∼ − × − / GeV/ c .Highly efficient charged particle tracking is achievedusing the pixel detector and main tracker to recognise andmeasure prompt tracks, in conjunction with the ECAL,which can identify short track stubs in its first few layersto catch tracks arising from secondary decays of long-lived particles. With the choice of a 5 T solenoidal mag-netic field, in part chosen to control the e + e − -pair back-ground, the design allows for a compact tracker design. To unravel the underlying physics mechanisms of newobserved processes, the identification of heavy flavourswill play a critical role. One of the main tools for heavyflavour identification is the vertex detector. The physicsgoals dictate an unprecedented spatial three-dimensionalpoint resolution and a very low material budget to min-0imise multiple Coulomb scattering. The running condi-tions at the ILC impose the readout speed and radia-tion tolerance. These requirements are normally in ten-sion. High granularity and fast readout compete witheach other and tend to increase the power dissipation.Increased power dissipation in turn leads to an increasedmaterial budget. The challenges on the vertex detectorare considerable and significant R&D is being carried outon both the development of the sensors and the mechan-ical support. The SiD vertex detector uses a barrel anddisk layout. The barrel section consists of five siliconpixel layers with a pixel size of 20 × µ m . The for-ward and backward regions each have four silicon pixeldisks. In addition, there are three silicon pixel disks ata larger distance from the interaction point to provideuniform coverage for the transition region between thevertex detector and the outer tracker. This configurationprovides for very good hermeticity with uniform coverageand guarantees excellent charged-track pattern recogni-tion capability and impact parameter resolution over thefull solid angle. This enhances the capability of the inte-grated tracking system and, in conjunction with the highmagnetic field, makes for a very compact system, therebyminimising the size and costs of the calorimetry.To provide for a very robust track-finding performancethe baseline choice for the vertex detector has a sen-sor technology that provides time-stamping of each hitwith sufficient precision to assign it to a particular bunchcrossing. This significantly suppresses backgrounds.Several vertex detector sensor technologies are beingdeveloped. One of these is a monolithic CMOS pixel de-tector with time-stamping capability (Chronopixel [149]),being developed in collaboration with SRI International.The pixel size is about 10 × µ m with a design goalof 99% charged-particle efficiency. The time-stampingfeature of the design means each hit is accompanied bya time tag with sufficient precision to assign it to aparticular bunch crossing of the ILC – thus the nameChronopixel. This reduces the occupancy to negligi-ble levels, even in the innermost vertex detector layer,yielding a robust vertex detector which operates at back-ground levels significantly in excess of those currentlyforeseen for the ILC. Chronopixel differs from the similardetectors developed by other groups by its capability torecord time stamps for two hits in each pixel while usingstandard CMOS processing for manufacturing. Followinga series of prototypes, the Chronopixel has been provento be a feasible concept for the ILC. The three prototypeversions were fabricated in 2008, in 2012, and in 2014.The main goal of the third prototype was to test possi-ble solutions for a high capacitance problem discoveredin prototype 2. The problem was traced to the TSMC 90nm technology design rules, which led to an unacceptablylarge value of the sensor diode capacitance. Six differentlayouts for the prototype 3 sensor diode were tested, andthe tests demonstrated that the high capacitance prob-lem was solved.With prototype 3 proving that a Chronopixel sensor can be successful with all known problems solved, opti-mal sensor design would be the focus of future tests. Thecharge collection efficiency for different sensor diode op-tions needs to be measured to determine the option withthe best signal-to-noise ratio. Also, sensor efficiency forcharged particles with sufficient energy to penetrate thesensor thickness and ceramic package, along with a trig-ger telescope measurement, needs to be determined. Be-yond these fundamental measurements, a prototype of afew cm with a final readout scheme would test the longertrace readout resistance, capacitance, and crosstalk.A more challenging approach is the 3D vertical inte-grated silicon technology, for which a full demonstrationis also close.Minimising the support material is critical to the de-velopment of a high-performance vertex detector. An ar-ray of low-mass materials such as reticulated foams andsilicon-carbide materials are under consideration. An al-ternative approach that is being pursued very activelyis the embedding of thinned, active sensors in ultra low-mass media. This line of R&D explores thinning activesilicon devices to such a thickness that the silicon be-comes flexible. The devices can then be embedded in,for example, Kapton structures, providing extreme ver-satility in designing and constructing a vertex detector.Power delivery must be accomplished without exceed-ing the material budget and overheating the detector.The vertex detector design relies on power pulsing dur-ing bunch trains to minimise heating and uses forced airfor cooling. The main tracker technology of choice is silicon strip sen-sors arrayed in five nested cylinders in the central regionand four disks following a conical surface with an angleof 5 degrees with respect to the normal to the beam-line in each of the end regions. The geometry of theendcaps minimises the material budget to enhance for-ward tracking. The detectors are single-sided silicon sen-sors, approximately 10 ×
10 cm with a readout pitchof 50 µ m. The endcaps utilise two sensors bonded back-to-back for small angle stereo measurements. With anouter cylinder radius of 1.25 m and a 5 T field, thecharged track momentum resolution will be better than δ (1 /p T ) = 5 × − /(GeV/ c ) for high momentum trackswith coverage down to polar angles of 10 degrees. A plotof the momentum budget as a function of polar angle isshown in Fig. 28.The all-silicon tracking approach has been extensivelytested using full Monte-Carlo simulations including fullbeam backgrounds. Besides having an excellent mo-mentum resolution it provides robust pattern recognitioneven in the presence of backgrounds and has a real safetymargin, if the machine backgrounds will be worse thanexpected.1 FIG. 28: Material in the SiD detector, in terms of fractionsof a radiation length, as a function of the polar angle.
The SiD baseline design incorporates the elements neededto successfully implement the PFA approach. This im-poses a number of basic requirements on the calorime-try. The central calorimeter system must be containedwithin the solenoid in order to reliably associate tracksto energy deposits. The electromagnetic and hadronicsections must have imaging capabilities that allow bothefficient track-following and correct assignment of en-ergy clusters to tracks. These requirements imply thatthe calorimeters must be finely segmented both longi-tudinally and transversely. In order to ensure that nosignificant amount of energy can escape detection, thecalorimetry must extend down to small angles with re-spect to the beampipe and must be sufficiently deep toprevent significant energy leakage. Since the average pen-etration depth of a hadronic shower grows with its energy,the calorimeter system must be designed for the highest-energy collisions envisaged.In order to ease detector construction the calorimetermechanical design consists of a series of modules of man-ageable size and weight. The boundaries between mod-ules are kept as small as possible to prevent significantnon-instrumented regions. The detectors are designedto have excellent long-term stability and reliability, sinceaccess during the data-taking period will be extremelylimited, if not impossible.The combined ECAL and HCAL systems consist of acentral barrel part and two endcaps, nested inside thebarrel. The entire barrel system is contained within thevolume of the cylindrical superconducting solenoid.SiD’s reliance on particle flow calorimetry to obtaina jet energy resolution of ∼
3% demands a highly seg-mented (longitudinally and laterally) electromagneticcalorimeter. It also calls for a minimized lateral elec-tromagnetic shower size, by minimizing the Moliere ra-dius to efficiently separate photons, electrons and chargedhadrons [150].The SiD ECal design employs thirty longitudinal lay-ers, the first twenty each with 2.50 mm tungsten alloy thickness and 1.25 mm readout gaps, and the last tenwith 5.00 mm tungsten alloy. The total depth is 26 ra-diation lengths, providing good containment of electro-magnetic showers.Simulations have shown the energy resolution for elec-trons or photons to be well described by 0.17 / √ E ⊕ − ) allows reducing the heat load using power puls-ing, thus allowing passive thermal management withinthe ECal modules.Bench tests of the KPiX bonded sensor with a cosmicray telescope trigger yielded a Landau distribution witha peak of the signal at about 4 fC is consistent withour expectation for minimum-ionizing particles (MIP)passing through the fully-depleted 320 µ m thick sensors.Crosstalk between channels has been managed and thenoise distribution shows an RMS of 0.2 fC, well below the4 fC MIP signal, and exceeding the ECal requirement.The overall mechanical structure of the ECal barrel hasbeen designed for minimal uninstrumented gaps. Inputpower and signals are delivered with Kapton flex cables.The KPiX chip has an average power less than 20 mW,resulting in a total heat load that is managed with a coldplate and water pipes routed into the calorimeter.A first SiD ECal prototype stack of nine (of thirty) lay-ers has been constructed and was exposed to a 12.1 GeVelectron beam at the SLAC End Station Test Beam Fa-cility. This data collection demonstrated good measure-ments of multiple particle overlap and reconstruction ofoverlapping showers [152]. Comparison of the depositedenergy distribution in each of the nine layers also agreeswell with simulations. An algorithm developed to countthe number of incident electrons in each event was usedto assess the ability of the calorimeter to separate twoshowers as a function of the separation of the showers,achieving 100% for separations of >
10 mm.The hadronic calorimeter has a depth of 4.5 nuclearinteraction lengths, consisting of alternating steel platesand active layers. The baseline choice for the active lay-ers is scintillator tiles read out via silicon photomultipli-ers. For this approach SiD is closely following the ana-log hadron calorimeter developments within the CALICEcollaboration. In this context, the simulated HCAL en-ergy resolution has been shown to reproduce well theresults from the CALICE AHCAL prototype module ex-posed to pion beams.2
Two special calorimeters are foreseen in the very forwardregion: LumiCal for a precise luminosity measurement,and BeamCal for the fast estimation of the collision pa-rameters and tagging of forward-scattered beam parti-cles. LumiCal and BeamCal are both compact cylindri-cal electromagnetic calorimeters centered on the outgo-ing beam, making use of semiconductor-tungsten tech-nology. BeamCal is placed just in front of the final focusquadrupole and LumiCal is aligned with the electromag-netic calorimeter endcap.LumiCal makes use of conventional silicon diode sensorreadout. It is a precision device with challenging require-ments on the mechanics and position control, and mustachieve a small Moliere radius to reach its precision tar-gets. Substantial work has been done to thin the siliconsensor readout planes within the silicon-tungsten assem-bly. Dedicated electronics with an appropriately largedynamic range is under development.BeamCal is exposed to a large flux of low-energyelectron-positron pairs originating from beamstrahlung.These depositions, useful for a bunch-by-bunch luminos-ity estimate and the determination of beam parameters,require radiation hard sensors. The BeamCal has tocope with 100% occupancies, requiring dedicated front-end electronics. A challenge for BeamCal is to identifysensors that will tolerate over one MGy of ionizing ra-diation per year. Sensor technologies under consider-ation include polycrystalline chemical vapor deposition(CVD) diamond (too expensive to be used for the fullcoverage), GaAs, SiC, Sapphire, and conventional sili-con diode sensors. The radiation tolerance of all of thesesensor technologies has been studied in a high-intensityelectron beam.For SiD, the main activities are the study of theseradiation-hard sensors, development of the first versionof the so-called Bean readout chip, and the simulationof BeamCal tagging for physics studies. SiD coordinatesthese activities through its participation in the FCALR&D Collaboration.
The SiD superconducting solenoid is based on the CMSsolenoid design philosophy and construction techniques,using a slightly modified CMS conductor as its baselinedesign. Superconducting strand count in the coextrudedRutherford cable was increased from 32 to 40 to accom-modate the higher 5 T central field.Many iron flux return configurations have been simu-lated in two dimensions so as to reduce the fringe field.An Opera 3D calculation with the Detector IntegratedDipole (DID) coil has been completed. Calculations ofmagnetic field with a 3D ANSYS program are in progress.These will have the capability to calculate forces andstress on the DID as well as run transient cases to checkthe viability of using the DID as a quench propagator for the solenoid. Field and force calculations with aniron endcap HCAL were studied. The field homogeneityimprovement was found to be insufficient to pursue thisoption.Conceptual DID construction and assembly methodshave been studied. The solenoid electrical power system,including a water-cooled dump resistor and grounding,was established. Significant work has been expended onexamining different conductor stabiliser options and con-ductor fabrication methods. This work is pursued as acost- and time-saving effort for solenoid construction.
The flux-return yoke is instrumented with position sen-sitive detectors to serve as both a muon filter and a tailcatcher. The total area to be instrumented is very sig-nificant – several thousand square meters. Technologiesthat lend themselves to low-cost large-area detectors aretherefore under investigation. Particles arriving at themuon system have seen large amounts of material in thecalorimeters and encounter significant multiple scatteringinside the iron. Spatial resolution of a few centimetres istherefore sufficient. Occupancies are low, so strip detec-tors are possible. The SiD baseline design uses scintilla-tor technology, with RPCs as an alternative. The scintil-lator technology uses extruded scintillator readout withwavelength shifting fibre and SiPMs, and has been suc-cessfully demonstrated. Simulation studies have shownthat nine or more layers of sensitive detectors yield ad-equate energy measurements and good muon detectionefficiency and purity. The flux-return yoke itself has beenoptimised with respect to the uniformity of the centralsolenoidal field, the external fringe field, and ease of theiron assembly. This was achieved by separating the barreland end sections of the yoke along a 30 degree line.
A time-efficient implementation of the push-pull modelof operation sets specific requirements and challengesfor many detector and machine systems, in particularthe interaction region (IR) magnets, the cryogenics, thealignment system, the beamline shielding, the detectordesign and the overall integration. The minimal func-tional requirements and interface specifications for thepush-pull IR have been successfully developed and pub-lished [153, 154]. All further IR design work on boththe detectors and machine sides are constrained by thesespecifications.
The ILD detector has been developed by a proto-collaboration with the goal to develop and eventuallypropose a fully integrated detector for the ILC.The ILD detector concept has been designed asa multi-purpose detector. It should deliver excel-lent physics performance for collision energies between3
FIG. 29: 3D-picture of the ILD detector.
90 GeV and 1 TeV, the largest possible energy reach ofthe ILC. The ILD detector has been optimized to per-form excellently at the initial ILC energy of 250 GeV(for more details see [5, 155]). An artist’s view of theILD detector is shown in Fig. 29.The science which will be done at the ILC requires adetector that truly covers all aspects of the e + e − events.The tracking philosophy is very different from that ofSiD, as will be discussed in a moment. However, simi-larly to SiD, the ILD detector has been designed to com-bine the traditional precision detector elements such asas vertex detectors and trackers in an overall design phi-losophy that optimizes jet reconstruction using particleflow. The high precision vertex detector positioned very closelyto the interaction point is followed by a hybrid trackinglayout, realised as a combination of silicon tracking witha time projection chamber, and a calorimeter system.The complete system is located inside a large solenoidproviding a magnetic field of 3.5-4 T. On the outside ofthe coil, the iron return yoke is instrumented as a muonsystem and as a tail catcher calorimeter.The vertex detector is realised as a multi-layer pixel-vertex detector (VTX), with three super-layers, eachcomprising two layers. The detector has a pure barrelgeometry. To minimise the occupancy from backgroundhits, the first super-layer is only half as long as the outertwo. Whilst the underlying detector technology has notyet been decided, the VTX is optimised for point resolu-tion and minimum material thickness.A system of silicon strip and pixel detectors surroundsthe VTX detector. In the barrel, two layers of silicon stripdetectors (SIT) are arranged to bridge the gap betweenthe VTX and the TPC. In the forward region, a system oftwo silicon-pixel disks and five silicon-strip disks (FTD)provides low angle tracking coverage.A distinct feature of ILD is a large volume time pro-jection chamber (TPC) with up to 224 points per track.The TPC is optimised for 3-dimensional point resolu-tion and minimum material in the field cage and in the / degrees θ -80 -60 -40 -20 0 X SEToutside TPCTPCSIT + FTDVXT
FIG. 30: Material in the ILD detector, in terms of fractionsof a radiation length, as a function of the polar angle. end-plate. It also allows d E /d x -based particle identifi-cation. At the ILC, a TPC has a number of specificstrengths which make this type of detector attractive.A time projection chamber offers true three-dimensionalpoints, and offers many of those along a charged particletrajectory. The intrinsic disadvantage of a TPC, its slowreadout speed, does not harm the performance at theILC, since the time between bunches is relatively long,around 300 ns. On the other hand the large number ofpoints offer superb pattern recognition capabilities, andallows the detailed reconstruction of kinks or decays inflight within its volume. This can be achieved at a verylow material budget, rather uniformly distributed overthe sensitive volume. The excellent performance of thesystem is particularly striking at low momenta, at a fewGeV and below, where the combination of three dimen-sional reconstruction and low material allows the efficientand precise reconstruction of tracks.Outside the TPC, a system of Si-strip detectors inbetween the TPC and the ECAL (SET), provide ad-ditional high precision space points which improve thetracking performance and provide additional redundancyin the regions between the main tracking volume and thecalorimeters.A key aspect of the ILD detector design is the low massof the tracking system. The total material as a functionof angle, in radiation lengths, is shown in Fig. 30. A highly segmented electromagnetic calorimeter (ECAL)provides up to 30 samples in depth and small transversecell size, split into a barrel and an end cap system. Forthe absorber, Tungsten has been chosen; for the sensitivearea, silicon diodes or scintillator strips are considered.This is followed by a segmented hadronic calorimeter(HCAL) with up to 48 longitudinal samples and smalltransverse cell size. Two options are considered, both4based on a steel-absorber structure. One option usesscintillator tiles of 3 × , which are read out with ananalogue system. The second uses a gas-based readoutwhich allows a 1 × cell geometry with a semi-digitalreadout of each cell.At very forward angles, below the coverage provided bythe ECAL and the HCAL, a system of high precision andradiation hard calorimetric detectors (LumiCAL, Beam-CAL, LHCAL) is foreseen. The LumiCAL and Beam-CAL are based on technologies developed in the contextof the FCAL collaboration. These detectors extend thecalorimetric coverage to almost 4 π , measure the lumi-nosity, and monitor the quality of the colliding beams.the LHCAL system bridges the electromagnetic endcapcalorimeter with the forward systems. A large volume superconducting coil surrounds thecalorimeters, creating an axial B -field of nominally 3.5-4 Tesla.An iron yoke, instrumented with scintillator strips orresistive plate chambers (RPCs), returns the magneticflux of the solenoid, and, at the same time, serves as amuon filter, muon detector and tail catcher calorimeter. The ILD detector is designed to operate in the ILC inter-action region with a push-pull scheme, allowing the rapidinterchange of ILD with SiD. Detailed studies have beendone to understand the impact this scheme might have onthe detector and its design. In addition the ILD detectoris optimised for operation in the seismic active region inthe north of Japan. Extensive simulation studies for themain components have shown that the detector is stableagainst seismic events.Key plots to evaluate the projected performances ofthe ILD and SiD detectors will be presented in the fol-lowing chapter. These plots will also illustrate the suc-cessive stages of event reconstruction from raw data andwill describe the level of detail that we have consideredin making these estimates of performance. As we havealready noted, the ILD and SiD detectors include manytechnologies that have been developed in close coopera-tion with R&D collaborations and have been extensivelytested. For both detectors, the performance numbers ofkey systems are based on results from prototypes, wher-ever possible, and extrapolated to the full detector per-formance. This strong check against experimental resultsensures that the performance numbers are reliable andare considered a realistic estimate of the ultimate detec-tor performance.
FIG. 31: Schematic view of the hierarchical EDM in LCIO.
7. COMPUTING, EVENT RECON-STRUCTION, AND DETECTOR PER-FORMANCE
This section will describe the software framework usedfor ILC event analysis, working from raw data or digitizedsimulation data to physics objects. We will first describethe core software tools used by the detector groups. Wewill then follow the path by which this software to used toprovide detailed detector models and model data sets, toreconstruct the data including as much realism as possi-ble, and to produce the final physics objects for analysis.At the successive stages of this process, we will illustratethe intermediate results with performance plots that alsocan be used to benchmark the detector models. Finally,we will discuss the computing concept and costs for theILC experiments.More than 15 years ago the linear collider communitystarted to develop common software tools to facilitate thedevelopment and optimization of detector concepts basedon realistic simulations of physics interactions. Thesesoftware tools eventually led to the creation of a commonsoftware ecosystem called iLCSoft [156]. The iLCSoft tools are used by both ILC detector concepts as well asby CLIC and partly by CEPC and FCC.From the start, a strong emphasis has been placed ondeveloping flexible and generic tools that can easily beapplied to other experiments or new detector concepts.This approach of developing common tools wherever pos-sible has helped considerably in leveraging the limitedmanpower and putting the focus on algorithm develop-ment that is crucial for the physics performance.
The foundation for the development of common soft-ware was laid with LCIO [157], the event data model(EDM) and persistency tool for linear collider studies.At the core of LCIO is a hierarchical EDM for any parti-cle physics experiment, as shown in Fig. 31. It providesdata classes for all phases of the event processing, starting5
FIG. 32: Schematic view of DD4hep with its maincomponents and interfaces. from Monte Carlo truth information, continuing to gen-erate raw data and digitization, and processing this tothe final reconstruction and analysis. Objects at higherlevels of the processing point back to the lower level con-stituting objects. As a specific design decision, there areno pointers back to the Monte Carlo truth but these canbe added if needed using dedicated generic LCRelationobjects. These relation objects can be used to createmany-to-many relations between arbitrary types in theEDM. A special class LCGenericObject holds user de-fined data in named vectors of types int, float and double.This feature is used in many test beams for conditionsdata and raw data from the DAQ. LCIO provides APIsin C ++ , Java and Fortran, but today C ++ is used almostexclusively.The C ++ application framework Marlin [158] providesan easy to use environment for developing software mod-ules on all levels of processing and uses LCIO as its tran-sient data format, i.e. all data that is read in or cre-ated by a software module (called Processor ) are storedin the
LCEvent class from LCIO. Marlin processors areself-documenting and controlled via xml-steering files.As processors have well defined input and output data,Marlin provides a ”Plug-And-Play” environment, whereany specific algorithm can easily be exchanged with an-other equivalent implementation for direct comparisonsand benchmarking.The generic detector description toolkit DD4hep [159,160] provides a powerful tool for describing the detectorgeometries, materials and readout properties. DD4hepfollows a modular component based approach and pro-vides interfaces to full simulations with GEANT4 [161]via DDG4, to reconstruction programs via DDRec andto conditions data and alignment with DDCond andDDAlign respectively, see Fig. 32. DD4hep is an excellentexample for the development of generic software tools forthe wider HEP community and was one of the first incu-bator projects adopted by the Hep Software Foundation.While it was developed to address the needs of the lin-ear collider community, it is now used by several otherprojects and is under evaluation by LHC experiments.
Energy (GeV) Energy (GeV)
124 124.5 125 125.5 1260100002000030000
FIG. 33: Beam energy spectra for √ s = 250 GeV Set-A,created with GuineaPig (blue-dashed: e − , red-solid e + ). Both detector concepts have created large, realisticMonte Carlo samples with the full Standard Modelphysics as well as various BSM scenarios that have beenused for the physics analyses presented in the follow-ing sections. In a first step, large generator sampleswith e + e − events are created with the Whizard [162]event generator. Whizard uses tree-level matrix ele-ments and loop corrections to generate events with thefinal state partons and leptons based on a realistic beamenergy spectrum, the so called hard sub-process . Thehadronization into the visible final state is performedwith Pythia [163] tuned to describe the LEP data.The input spectrum is created with Guinea-Pig [164], adedicated simulation program for computing beam-beaminteractions at linear colliders. The two dominating ef-fects of the strong beam-beam interactions are beam-strahlung, leading to the available luminosity spectrum(see Fig. 33), and the creation of incoherent e + e − -pairsthat are the source of the dominant background at theILC. These electrons and positrons are predominantlycreated in a forward cone as shown in Fig. 34. It is thiscone that restricts the minimal allowed radius of the in-nermost layer of the vertex detector.Another source of background at the ILC are γγ → hadrons events, due to bremsstrahlung and beam-strahlung photons. These types of events are generatedfor γγ cms-energies from 300 MeV to 2 GeV with a ded-icated generator based on Ref. [166]; for higher energiesPythia is used.6 FIG. 34: Cone of background from incoherent e + e − -pairs,generated with Guinea-Pig and simulated in the 5 T B-fieldof the SiD detector (from [165]).FIG. 35: Cut-away view of the tracking system asimplemented in the SIDLOI3 simulation model (from [5]).
Both detector concepts have adopted DD4hep for de-scribing their detector simulation models and use ddsim ,a python application that is based on the DDG4 com-ponent, to provide a gateway to full simulations withGEANT4. In DD4hep the detector geometry is imple-mented in dedicated C ++ modules for every subdetectorand the actual parameters with dimensions and materialsare provided via compact xml-files. DD4hep contains alarge palette of predefined sub-detector drivers, allowingfor an easy implementation of a new detector concept byproviding suitable compact files. A dedicated softwarepackage lcgeo [167], which is shared by SiD, ILD andCLICdp, contains all subdetector drivers for the detec-tor concepts under study by these groups, together withthe corresponding compact parameter files.Both detector concept groups have invested consider-able effort into making their full-simulation models asrealistic as possible, by • following the exact dimensions and layout of detec-tor elements from engineering models • implementing correct material properties • implementing precise descriptions of the actual de-tector technology • adding realistic amounts of dead material from sup-ports and services, such as cables and cooling pipes • introducing realistic gaps and imperfections intothe subdetectorsCare has been taken to include realistic material esti-mates in particular in the tracking region where the ma-terial budget has a direct impact on the detector per-formance. Figure 35 shows the tracking detector as im-plemented for the SiD simulation model. The averagematerial budget in the tracking volume of the simulationmodels has already been shown in Sec. 6, Figs. 28 and 30,for SiD and ILD respectively.Before the two concepts had decided to move tothe common geometry description and simulation withDD4hep, they had implemented their detailed simula-tion models in Mokka [168] and slic [169]. These modelshave been ported into DD4hep preserving all featuresand dimensions, thus resulting in equivalent simulationresults. Most of the physics analyses in the next sectionsare based on simulations using these older programs.The high level of detail in the simulation models asdescribed above is a key prerequisite for the realistic un-derstanding of the expected detector performance andthe physics reach of the ILC for both detector concepts. The output of the detailed full simulations withGEANT4 from ddsim are
SimTrackerHit and
Sim-CalorimeterHit objects. These store the deposited en-ergy in the sensitive detector elements, such as siliconwafers and calorimeter cells, together with the positionand pointers to the
MCParticle that created the energydeposition. In the digitization step, carried out in ded-icated Marlin processors, these hits are converted into
TrackerHit and
CalorimeterHit objects, taking into ac-count all relevant effects from the detector and the read-out electronics.The
SimTrackerHits contain the exact energy-weighted position of the individual energy depositions ina given sensitive detector element. For silicon strip-andpixel detectors as well as the ILD-TPC, these positionsare smeared according to resolutions that have been es-tablished from test beam campaigns for the different sen-sor technologies, thereby including effects from chargesharing, clustering and position reconstruction. Table Xshows the point resolution parameters used for ILD.In the TPC hit digitization, simulated hits that arecloser than the established double-hit resolution of 2 mm7
Subdetector Point ResolutionVTX σ rφ,z = 2 . µ m (layer 1) σ rφ,z = 6 . µ m (layer 2) σ rφ,z = 4 . µ m (layers 3-6)SIT σ α z = 7 . µ m α z = ± . ◦ (angle with z-axis)SET σ α z = 7 . µ m α z = ± . ◦ (angle with z-axis)FTD σ r = 3 . µ m Pixel σ r ⊥ = 3 . µ mFTD σ α r = 7 . µ m Strip α r = ± . ◦ (angle with radial direction)TPC σ rφ = (cid:0) + 900 sin φ + (cid:0) (25 / × (4 T /B ) sin θ (cid:1) ( z/ cm) (cid:1) µ m σ z = (400 + 80 × ( z/ cm)) µ m where φ and θ are the azimuthal andpolar angle of the track directionTABLE X: Effective point resolutions as used in thedigitization of the ILD tracking detectors. Theparameterization for the TPC takes into account geometriceffects due to the direction of the track with respect to thepad row and has been established from test beam data. in rφ and 5 mm in z are merged into one. For the sili-con detectors this treatment is not necessary, due to theexpected low occupancies.The SimCalorimeterHits contain the total energy de-posited in each calorimeter cell, together with the indi-vidual depositions from the individual Monte Carlo steps.For scintillating calorimeters Birk’s Law is already ap-plied during the simulation, resulting in different lightyields for different particles. Dedicated digitizers takeinto account effects of non-uniformity of the light yieldfor scintillators as well as cross-talk between neighboringchannels. The latter is important in particular for thesimulation of (semi)-digital calorimeters using RPCs andis possible due to the availability of the individual simu-lation steps, containing the exact position of the energydeposition.During the calorimeter digitization, a two step calibra-tion is applied for every calorimeter type and samplingstructure. In a first step the hits are calibrated to a MIPsignal and in a second step, the total energy is calibratedto an absolute value of the cell energy in GeV. This cal-ibration is an iterative procedure, based on the applica-tion of the full particle flow algorithm to single particleevents with photons and K s and thereby repeatedly ad-justing the calibration constants. The first step of the event reconstruction consists of iden-tifying the trajectories of charged particles based on the
FIG. 36: Schematic view of the MarlinTrk tracking toolsavailable in iLCSoft. They are based on the LCIO eventdata model and the DDRec geometry description. positions of their energy depositions in the detector (
Sim-TrackerHits ), typically referred to as pattern recognition .In a second step the kinematic parameters of these trajec-tories are fitted based on the known equations of motionin a magnetic field and the errors of the hit positions.Often both steps are carried out together, e.g. , by usinga Kalman-Filter and simply referred to as
Tracking .The tracking packages in iLCSoft is called MarlinTrkand provides a generic tracking-API
IMarlinTrk and un-derlying fitting code, using the Kalman-Filter package
KalTest [170]. The
IMarlinTrk interface provides code toiteratively add hits to a track segment, thereby updatingthe track parameters, extrapolation of the current trackstate to the next measurement surface or any given pointin space. It uses LCIO as data model for the Track andTrackState with a perigee track parameterization withtrack curvature ω , impact parameters d and z and di-rection parameters φ and tan( λ ). A palette of differentpattern recognition algorithms are programmed against IMarlinTrk as shown in Fig. 36. ILD uses the followingdifferent algorithms in the different parts of the trackingregion (for more details see Ref. [171]): • SiliconTrackingAlgorithm used in the innermost Si-tracking detec-tor VXD and SIT, based on a brute-force tripletseeding followed by a road search using the extrap-olation to the next layer provided in MarlinTrk. • ForwardTrackingStand alone pattern recognition in the FTD for-ward tracker using a Cellular-Automaton to find a(possibly large) set of track candidates that are re-duced to a unique and consistent set through theuse of a Hopfield Network. • ClupatraPattern recognition algorithm for the TPC, basedon topological clustering in the outer TPC padrow layers for seeding, followed by a Kalman-Filterbased road search inwards. • FullLDCTrackingA collection of algorithms for merging track seg-ments from the previous algorithms and assign-8ments of leftover hits followed by a final re-fit usinga Kalman-Filter.SiD had originally developed their stand-alone track-ing software in the Java framework
LCSim [172] usinga triplet based seeding followed by a road search and afinal track fit. More recently SiD has adopted the
Confor-malTracking algorithm originally developed for CLICdp.It uses a conformal mapping transforming circles goingthrough the origin (IP) into straight lines which are thenidentified using a Cellular-Automaton.The correct reconstruction of the kinematics of chargedparticles requires a sufficiently detailed description of thematerial the particles have traversed, in order to correctlyaccount for effects of energy-loss and multiple-scatteringin the fit. The DD4hep component DDRec provides ded-icated surface classes for track reconstruction and fitting.These surface classes provide the geometric informationof the corresponding measurement surfaces as well as ma-terial properties, averaged in a suitable way. Surfaces arealso used to account for effects from dead material layers,such as support structures or cables and services.The resulting tracking efficiencies for the ILD detectorare shown as a function of the momentum and cos( θ ) inFig. 37.The normalised transverse momentum resolution σ (1 /p T ) for single-muon events the SiD detector modelis shown in Fig. 38 together with fits using the parame-terisation: σ ( p T ) p T = a ⊕ bp sin θ (15)Comparable results are obtained for ILD, and bothdetector concepts achieve their design goals for the mo-mentum resolution of σ ( p T ) /P T < × − GeV − forhigh momentum central tracks.The impact parameter resolution as a function of polarangle for single-muon events in SiD is shown in Fig. 39for different particle momenta. A resolution of a few µ mis achieved for high mometum tracks over a large rangeof the polar angle down to ∼ o .The tracking software is completed with dedicatedprocessors for the identification and reconstruction ofkinks and V s. Tracks with kinks can arise frombremsstrahlung, typically for electrons, or a large angledeflection due to multiple scattering. V s are almost ex-clusively decays of K s and Λ and gamma conversions. The particle flow algorithm (PFA) aims at reconstructingevery individual particle created in the event in order totake the best available measurement for the given particletype: • charged particlesusing the momentum measured in the tracking FIG. 37: Tracking efficiency for tt -events at √ s = 500 GeVin the ILD detector as a function of momentum(cos( θ ) > .
99) [upper] and cos( θ ) ( p > d IP <
10 cm). Decays in flight are excludedand tracks are required to have left at least 4 hits in thedetector. Background from e + e − -pairs for two bunchcrossings is overlaid to the tt -events. detectors with the excellent resolution describedabove. • photonsmeasured in the Ecal with an energy resolution of σ ( E ) /E ∼ / (cid:112) ( E/ GeV). • neutral hadronsmeasured predominantly in the HCAL with an en-ergy resolution of σ ( E ) /E ∼ / (cid:112) ( E/ GeV). Hadronic showers often start in the ECAL and might extend intothe Muon system. This is taken into account in PandorPFA. FIG. 38: Normalised transverse momentum resolution forsingle-muon events as function of momentum in the
SIDLOI3 simulation model (from [5]). The dashed lines arefits to the data points according to eq. 15.FIG. 39: Impact parameter resolution σ ( d ) for single-muonevents as function of polar angle in the SIDLOI3 simulationmodel (from [5]).
The best jet energy measurement in hadronic eventswould be achieved if the above algorithm would workperfectly. However in reality there is always confusionin the assignment of individual
CalorimeterHits to Clus-ters and showers as well as in the assignment of tracks toclusters. This effect is demonstrated in Fig. 40 for Pan-doraPFA [173], the implementation of PFA available iniLCSoft that is used by both detector concepts.The input to PandoraPFA are collections of Tracks,Kinks, V s and collections of all digitized Calorime-terHits together with some geometrical information re-trieved from DDRec. Following [173] the main steps ofthe algorithm are: • CalorimeterHits are clustered using a simple cone-
FIG. 40: Jet energy resolution (in %) for Z (cid:48) events as afunction of the jet energy in a realistic detector forPandoraPFA. Also shown are the effect of confusion and theresult assuming perfect PFA (from [173]). based algorithm, seeded either from isolated hits inthe first calorimeter layers or by the projection ofTracks to the front face of the ECAL. • the clustering algorithm is configured to prefersplitting of clusters rather than risking to falselymerge particles into single clusters. • Clusters are associated to Tracks based on topologi-cal (position and direction) and kinematic (momen-tum and energy) consistency. In case of significantdiscrepancies a re-clustering is initiated. • Clusters without associated Tracks are transformedinto neutral
ReconstructedParticles unless they canbe more likely interpreted as fragments of chargedparticles. • consistent Track-Cluster combinations are trans-formed into charged ReconstructedParticles . • particle identification plugins are applied to labelspecific particle types, such as photons, electronsand muons. • a dedicated weighting procedure known as softwarecompensation is applied to the hits inside a clusterin order to equalize hadronic and electromagneticshower components.The final output collection of PandoraPFA is a set ofobjects called “PandoraPFO”s. This represents the fi-nal output of the Reconstruction process. This collec-tion is either directly used for physics analyses or servesas input to higher-level reconstruction algorithms wherenecessary.0 [GeV] jet E
50 100 150 200 250 ) [ % ] j ( E ) / M ean j ( E R M S ILD Preliminary
ILD_l5_v02
50 100 150 200 250 ) [ G e V ] j ( E M ean ILD Preliminary
ILD_l5_v02 [GeV] jet E
50 100 150 200 2500.05 - FIG. 41: Upper: Jet energy resolution for Z → u, d, s eventsas a function of the jet energy in the standard ILDsimulation model. Lower: The resulting jet energy scale forthe same events. Fig. 41 shows the jet energy resolution and jet energyscale that is achieved for two variants of the ILD detec-tor for a dedicated event sample of hadronic Z → u, d, s events. The jet energy resolution is evaluated using RM S ( E ), the root mean square of the energy of thecentral 90% of the events. The restriction to u, d, s quarksis chosen to focus on the detector and PFA performancewithout the extra complication of missing energy due toneutrinos. After having reconstructed all of the individual parti-cles in the event, the next step in the processing is thereconstruction of primary and secondary vertices. This iscarried out in iLCSoft with the LCFIPlus [174] packagethat is also used for the tagging of heavy flavor jets.The primary vertex of the event is found in a tear-down procedure. First an initial vertex is fitted by a χ -minimization using all charged tracks in the eventand a constraint from the expected beam spot ( σ x =516 nm , σ y = 7 . , σ z ∼ µ m at E cms = 250 GeV).Then all tracks with a χ -contribution larger than a giventhreshold value are removed.In a second step LCFIPlus tries to identify secondaryvertices, starting out from forming all possible track-pairsfrom tracks not used in the primary vertex. The pairshave to fulfill suitable requirements with respect to theirinvariant mass, momentum direction and χ . V s areexcluded from these initial pairs. Secondary vertices arethen formed using so far leftover tracks in an iterativeprocedure and eventually adding compatible tracks orig-inally used in the primary vertex.Secondary vertices and optionally isolated leptons canbe used by LCFIPlus for jet clustering, aiming at highefficiency for correctly identifying heavy flavor jets. Theactual jet clustering is then performed by using a cone-based clustering with a Durham-like algorithm. Alter-natively users can use k T jet clustering algorithms fromFastjet [175], which is interfaced to Marlin in a dedicatedpackage MarlinFastJet.LCFIPlus also provides algorithms for jet flavor tag-ging using boosted decision trees (BDTs) based on suit-able variables from tracks and vertices. Fig. 42 showsthe mis-identification efficiency for jets from light quarksand c-quarks as a function of the b-tagging efficiency forthe SiD detector using LCFIPlus.There is a large palette of additional high level recon-struction algorithms available in iLCSoft addressing theneeds for physics analyses, e.g. • particle identification using dE/dx, shower shapesand multi-variate methods • γγ -finders for the identification of π s and η s • reconstructed particle to Monte-Carlo truth linkerfor cross checking analysis and reconstruction effi-ciencies • tools for jet clustering using Monte-Carlo truth in-formation • processors for the computation of various eventshapes In addition to the full simulation and reconstructionoutlined in the previous sections, there is a need for sim-ulation that can quickly generate substantial samples of1
FIG. 42: Mis-identification efficiency of light quark jets (redpoints) and charm jets (green points) as beauty jets versusbeauty identification efficiency in di-jets events at √ s = 91 GeV (from [5]). simulated and reconstructed events. Situations wherethis is desirable include detector optimisation and newphysics searches. In these cases, similar processes needto be simulated and reconstructed at a, possibly verylarge, number of different conditions. In the first case,one needs to modifying various aspects of the detectorin steps, in the latter, one needs to explore the entireallowed parameter space of a theory for new physics. Inaddition to these cases, fast simulation is also an assetfor simulating high cross section SM processes, such as γγ processes, where the investment in processor powerand intermediate storage might be prohibitively large toattain the goal that simulation statistics should be a neg-ligible source of systematic uncertainty.To meet these needs, a fast simulation program needsto be fast, flexible, and accurate. The SGV program[176]used at ILC meets these needs. The time to simulate andreconstruct an event is similar to the time it takes to gen-erate it ( ∼ −
10 ms). The response of the detector isas far as possible calculated from the detector design (sothere is no need to parametrisise pre-existing full simula-tion results). SGV has been shown to compare well bothwith full simulation and with real data [177].The program uses a simplified “ cylinders-and-discs ”description of the detector, which is used to calculatethe Kalman-filtered track-helix covariance matrix of eachgenerated charged particle. By Cholesky decompositionof the covariance matrix, the track-parameters are sim-ulated in a way such that all correlations are respected.The calorimetric response is calculated from the expectedsingle-particle performance of the different componentsof the calorimetric system, for each particle impingingon it. Optionally, the effects of shower-confusion can be included. To reduce the needed storage for a Giga-eventsize sample, event filtering can be applied at differentsteps of the processing, directly after generation, afterthe detector response is known, or after higher-level eventanalysis is done. Events passing all filters are output inLCIO DST-format, and can seamlessly be further anal-ysed within the Marlin framework.
An initial computing concept for the ILC, including afirst estimate of the required resources, has been devel-oped by the LCC Software and Computing Group.The foreseen computing concept follows in generalterms that of the current LHC experiments and Belle II,with a strong on-site computing center complemented bylarge Grid-based computing resources distributed aroundthe world. This concept is schematically shown in Fig. 43.Due to the much lower event rates at the ILC comparedto the LHC, we will be able to run in an un-triggeredmode in which collision data from every bunch crossingwill be recorded. At the experimental site, we requireonly limited computing resources for online monitoring,QA and data-buffering for a few days.Prompt reconstruction, event building, and filtering ofthe interesting collisions will be performed at the mainILC campus. A small fraction of the initial raw data willbe distributed to major participating Grid sites in theworld for further skimming and final redistribution forphysics analysis. A copy of the raw data from all bunchcrossings will be kept to allow for future searches for newexotic signatures.
Based on our detailed physics and background simula-tions, we estimate the total raw data rate of the ILC tobe ∼
8. PHYSICS SIMULATIONS: HIGGS
The physics case for the precision study for the Higgsboson presented in Section 4 will be realized through themeasurement of total cross sections and σ · BR valuesfor the various final-states. The major Higgs produc-tion cross sections at the ILC are shown in Fig. 44 as afunction of centre of mass energy for the optimal choice(-80%/+30%) of ILC beam polarisations. In Tab. XI, wepresent our estimates for the statistical errors that will be2 FIG. 43: Computing concept foreseen for the ILC, distributed over on-site computing at the interaction region, the maincampus and Grid-like offline computing. obtained for the total cross section for e + e − → ZH andfor the σ · BR s for this process and the W W fusion pro-cess, for a reference luminosity sample of 250 fb − andfor three different ILC energies. There is a similar tablefor the opposite beam polarisation state (+80%/-30%).In this case, the errors for ZH observables are almostthe same, due to a compensation of lower backgroundand lower signal cross sections. The W W fusion processhas a much reduced cross section and comparably lowerprecision[3]. These estimates are based on full-simulationanalyses using the tools presented in Sec. 7. The purposeof this section is explain how these numbers are obtained,what the factors are that limit them, and how these lim-itations might be relaxed.We begin with the observation that precision Higgs measurements will be much easier to obtain at a lep-ton collider than at a hadron collider. Table XII givesthe typical signal efficiencies for ILC analyses and thecorresponding signal to background ratios (S/B) after fi-nal cuts. The difference with LHC can be clearly seenusing the example of H → bb measurements. The de-cay of H → bb has been discovered by ATLAS andCMS [178, 179] with a significance of 5.4 σ , 5.5 σ , re-spectively, after producting about 4 million Higgs eventsper experiment. At the ILC, with only 400 Higgs eventswhich will be produced with an integrated luminosity of1.3 fb − (corresponding to 2 days of running time), thedecay of H → bb will be measured with a similar sig-nificance, around 5.2 σ according to the full simulationresult [180]. The S/B ratios for these analyses are il-3 FIG. 44: Cross sections for the three major Higgs productionprocesses as a function of center of mass energy, from [138]. - - - - - - - log E v en t s / . Data =1.16) m (b b fi VH, H ttSingle topZ+jetsMultijetW+jetsDiboson
ATLAS -1 = 13 TeV, 79.8 fbs - - - - - - - log05 P u ll ( s t a t. ) FIG. 45: Upper: signal H → bb and background events indifferent categories of S/B measured by ATLAS [178, 179]using LHC Run 2 data; lower: signal h → bb andbackground events in the bb mass spectrum expected fromthe ILC full simulation [180]. -80% e − , +30% e + polarization:250 GeV 350 GeV 500 GeV Zh ννh Zh ννh Zh ννhσ h → invis. h → bb h → cc h → gg h → W W ∗ ∗ h → τ τ ∗ ∗ h → ZZ
18 25 ∗ ∗ ∗ ∗ h → γγ ∗ ∗ ∗
47 27 h → µµ
72 87 ∗ ∗
120 100 a ∗ b ∗ ρ ( a, b ) -99.17 -95.6 ∗ -84.8TABLE XI: Projected statistical errors, in %, for Higgsboson measurements. The errors are quoted for luminositysamples of 250 fb − for e + e − beams with -80% electronpolarization and +30% positron polarization. Except for thefirst and last segments of each set, these are measurementsof σ · BR , relative to the Standard Model expectation. Thetop lines gives the error for the total cross section relative tothe Standard Model and the 95% confidence upper limit onthe branching ratio for Higgs to invisible decays. Thebottom lines in each half give the expected errors on the a and b parameters and their correlation (all in %) for e + e − → Zh (see (21). All error estimates in this table arebased on full simulation, and the entries marked with a ∗ areextrapolated from full simulation results.measurement efficiency S/B final. σ Zh in µ + µ − h
88% 1/1.3 BR ( h → bb ) in qqh
33% 1/0.89 BR ( h → τ τ ) in qqh
37% 1/0.44 BR ( h → W W ) in ννh
20% 1/1.6TABLE XII: Typical signal efficiencies (second column) andsignal over background ratio (S/B) after the final cuts (thirdcolumn) for some of the representative Higgs measurements(first column) at the ILC. lustrated in Fig. 45. Clearly, if one wishes to measurethe rate for h → bb , there are strong advantages in start-ing from a situation in which the signal stands well aboveany background process that would need to be controlled.The challenge of physics at a linear collider is to makeuse of this advantage in the most optimal way and realizethe potential to achieve very high precision.A full simulation analysis contains two components.The first is the detector simulation. This provides therealistic interactions between each final state particle andany part of the detector that the particle passes through,including creation of new particles during the interaction;concrete algorithms for tracking, particle flow analysis,vertex reconstruction and particle identification; the re-sulting performance of the various detector resolutionsfor track momentum, jet energy, and impact parameters;4and the efficiencies for tracking, flavor tagging, and iso-lated lepton finding. These aspects have already beendescribed in Section 7. The second component is theevent seletion, that is, the algorithms for discriminatingbetween signal and background events. That will be ourmain concern in the discussion of this section.First, however, we would like to emphasize to thereader a number of effects that are included in the de-tector modelling and event generation, and that must beincluded for a solid estimate of detection efficiencies andsignal-background discrimination: • beamstrahlung and ISR are implemented in theevent generators for both signal and backgroundprocesses. These effects are important for estima-tion of signal and background contributions in theanalyses that make use of the nominal value of thecentre-of-mass energy. A representative example isseen in Section 8.2.1, Fig. 46, for the determinationof the Higgs boson mass from Z recoil. Both beam-strahlung and ISR effects will drag signal eventsfrom the more sensitive peak region to the less sen-sitive tail region, and at the same time will inducemore background contribution in the signal region. • overlay of beam background events is implementedin every signal and background event sample. Thiswill affect the performance of reconstructed vari-ables related to jets and hence degrades the signaland background discrimination. There is a methodto partially remove the effect of this events whichwill be introduced in next section. • full Standard Model background is checked in allof the analyses to be described, in order not tomiss any significant contribution. For example, 2-fermion events developed with a parton shower canbecome background for the 4-fermion signal. An-other example is the background contribution toHiggs observables that comes from tail of the Breit-Wigner structure of a Z boson in e + e − → ZZ . It isnot correct neither to neglect the Z natural widthnor to ignore the similar diagram with the γ prop-agator. • explicit jet clustering and jet paring algorithms areused in all analyses. These often become the limit-ing factors in the analyses with 4 or more jets in thefinal state. The confusion between two color sin-glets, for instance Z and h in e + e − → Zh → jets ,could produce a much wider spread of the recon-structed dijet invariant mass than that due to thepure detector resolution. Hence, simply smearingthe dijet mass variable at the parton level accordingto the detector resolution is often too optimistic. • control of systematics is taken into account in thedesign of every selection cut.This section is organized as follows. In Sec. 8.1, we willintroduce the common procedures for event selections. Section 8.2 will discuss the analyses for the main Higgsobservables. The analysis strategies and selection cuts insome representative channels will be discussed in greatdetail. Section 8.4 presents some estimates for improve-ment of the key algorithms in the future. Section 8.5gives a dedicated discussion of the measurement of Higgsself-coupling. The full simulation analysis at the event selection levelcan be described in two steps: pre-selection and final-selection . At the pre-selection step each signal event ischaracterized according to its final states at parton levelby numbers of isolate leptons (meaning electron or muonunless otherwise stated), isolated taus, isolated photonsand jets, and nature of missing momentum. Here iso-lated particle is meant to be not coming from a jet. Theprocedures for the pre-selection are typically as follows: • isolated lepton finder , which will try to recon-struct the isolated leptons in each event. Themain algorithms are implemented in the proces-sor called IsolatedLeptonTagging in the iLCSoft,based on a multivariate method. It starts with se-lecting energetic electron/muon (momentum P > E ecal /E tot , E tot /P , E yoke , where E ecal ( E hcal ) isthe energy deposited in ECAL (HCAL), E tot isthe sum of E ecal and E hcal , and E yoke is the en-ergy deposited in Yoke. For electron, it is requiredthat E ecal /E tot > . . < E tot /P < . E tot /P < . E yoke > . • isolated tau finder , which will try to reconstructthe isolated taus. The main algorithms are imple-mented in TaFinder in the iLCSoft. It starts withfinding the most energetic charged particle as a taucandidate. Then the remaining most energetic par-ticle which is within a cone of cos θ = 0 .
99 aroundthe tau candidate will be combined to the tau can-didate if the invariant mass of the combined taucandidate does not exceed 2 GeV. This combin-ing step will be iterated until there is no any moreparticle to combine. The resulting combined taucandidate is identified as an isolated tau.5 • isolated photon selection , which will try to recon-struct the isolated photon. A photon is first identi-fied based on its cluster properties by PandoraPFA.For most of the signal processes with an isolatedphoton, it is usually sufficient to tag the most ener-getic photon which has energy larger than severaltens of GeV, as the candidate isolated photon. Ifthere are other photons within a very small cone ofcos θ = 0 .
999 around the candidate photon, thoseother photons are most probably split ones henceare merged into the candidate photon. • overlay removal , which will try to remove the pile-up beam background events in every event. Anexclusive jet clustering is performed using longitu-dinal invariant k t algorithm [181] for all the parti-cles except the selected isolated lepton/tau/photonin above step. As a result, the particles from beambackground events, which usually have very low- p t ,are clustered into beam jets and are effectively re-moved by the exclusive jet clustering process. Theinput parameters such as R and number of requiredjets are carefully optimized for each signal process.Alternative algorithms include anti- k t [182] and Va-lencia [183]. • jet clustering and flavor tagging , are done usingLCFIPlus as introduced in 7.6. All the particlesbelonging to the jets obtained in previous stepare then re-clustered into a few jets using anotherinclusive jet clustering algorithm, Durham algo-rithm [184]. Each jet is flavor tagged using thereconstructed information of its secondary and ter-tiary vertices.At the final-selection step, the reconstructed leptons,taus, photons and jets will be first combined to recon-struct W , Z , h or top according to the signal. Then var-ious cuts will be applied to further suppress backgroundevents. Details are explained measurement by measure-ment in the following. Unless stated otherwise, the anal-ysis is done at √ s = 250 GeV, a nominal integrated lu-minosity of 250 fb − is assumed, and the cuts and re-sults are illustrated with left-handed beam polarization e − L e + R : P ( e − , e + ) = ( − . , +0 . √ s or right-handed beam polarization e − R e + L : P ( e − , e + ) = (+0 . , − .
3) has a significant impacton the results. The results are straightforwardly extrap-olated into that for the running scenario introduced inSec. 3 and are then used as input for the Higgs couplingdetermination by a global fit introduced in Sec. 4. Thefull information for the uncertainties of Higgs observablesfor e − L e + R and e − R e + L can be found in Tab.6 of Ref. [3]. m h and σ Zh The signal processes are e + e − → Zh , Z → l + l − or qq and h → anything. Thanks to the known four momenta of initial states, the four momentum of final state h can bereconstructed as the recoil against the four momentumof Z , which is directly measured from its decay prod-ucts l + l − or qq . The mass of h ( m X ) can therefore bereconstructed as m X = s + m Z − E Z √ s, (16)where m Z and E Z are measured mass and energy of Z respectively. The signal events can hence be tagged with-out looking at the decay products of h . This techniqueis traditionally called recoil mass technique, and the twotypes of signal processes ( Z → l + l − and Z → qq ) arecalled leptonic recoil and hadronic recoil channels. Therecoil mass technique makes possible the measurementof the inclusive cross section of e + e − → Zh ( σ Zh ), thatplays a unique role in the determination of the absolutevalues of Higgs couplings as explained in Sec. 4. Mean-while, the Higgs mass ( m h ) can be straightforwardly de-termined by the m X spectrum. The detailed analysesfor leptonic recoil channels µ + µ − h and e + e − h and forhadronic recoil channel qqh can be found respectively inreferences [185] and [186–188]. For simplicity only theanalysis for µ + µ − h channel is illustrated in detail here.The event pre-selection in µ + µ − h channel starts withrequiring at least two isolated muons with oppositecharges and invariant mass ( m ll ) consistent with the Z mass (in the range m ll ∈ [50 , h → ZZ ∗ /W W ∗ /τ + τ − → µ + µ − + X . To minimize thepossibility of this case, or to maximize the possibilitythat the candidate muon pair is indeed from the primary Z decay, the following strategy is taken: when there aremore than one such candidate muon pairs, the pair whichminimizes following χ χ = ( m ll − M Z σ Z ) + ( m X − M h σ h ) (17)is identified as from the primary Z decay. Here M Z is 91.2 GeV, M h is 125 GeV, σ Z and σ h are resolu-tions for Z mass and recoil mass reconstructions. Af-ter the pre-selection, the remaining background eventsare dominated by leptonic and semi-leptonic decays of e + e − → ZZ , leptonic decay of e + e − → W W , and lep-tonic decay of e + e − → γZ .In the final selection, the cuts p llT >
10 GeV and | cos θ mis | < .
98, where p llT is the transverse momen-tum of muon pair and θ mis is the polar angle of missingfour momentum, are applied to suppress γZ backgroundevents. E vis >
10 GeV, where E vis is the visible en-ergy other than the muon pair, and m ll ∈ [73 , W W background events. ZZ aswell as W W and γZ background events are further sup-pressed by a dedicated BDT cut which is trained usingdistributions of polar angle of each muon, angle betweentwo muons, and polar angle of the muon pair. After a fi-nal cut that requires m X ∈ [110 , ) Recoil Mass (GeV/c
110 120 130 140 150 E v en t s + X @ 250 GeV µ + µ → +e + e Toy MC DataSignal+BackgroundSignalBackground
FIG. 46: Recoil mass spectrum against Z → µ + µ − for signal e + e − → Zh and SM background at 250 GeV [185]. ) Recoil Mass (GeV/c
100 150 200 250 E v en t s + X @ 500 GeV µ + µ → +e + e Toy MC DataSignal+BackgroundSignalBackground
FIG. 47: Recoil mass spectrum against Z → µ + µ − for signal e + e − → Zh and SM background at 500 GeV [185]. signal and background events are shown in the m X spec-trum in Fig. 46 for the Z → µ + µ − channel, where thesignal peak is clearly seen. The overall signal efficiencyis 88%, with an average signal over background ratio of1/1.3.The number of signal events and its statistical uncer-tainty are obtained by fitting m X spectrum with signalcomponent modeled by a kernel function and backgroundcomponent modeled by a third order polynomial, shownin Fig. 46. As shown by the green histogram in Fig. 46,the signal spectrum has a considerable non-Gaussian tailin the high mass end, which is due to the overestimateof effective √ s (cid:48) in e + e − → Zh reaction when beam-strahlung and ISR effects are included, recall Eqn. 16.It’s worth noting that these effects become so significantat √ s = 500 GeV, as shown in Fig. 47, that the measure-ment uncertainty could be underestimated by a factor of2 if the effects are not properly included in the simula-tion.For e − L e + R , the estimate of relative uncertainty on σ Zh measurement ( δσ Zh ) is 2.5% for the leptonic recoilchannel, where the contribution from e + e − h channel is slightly smaller than µ + µ − h channel due to the higherelectron bremsstrahlung. For e − R e + L , δσ Zh is estimatedto be 2.9%. By combining the hadronic recoil channel, δσ Zh is estimated to be 2.0% for both e − L e + R and e − R e + L ,as shown in Tab. XI. The enabled measurement of left-right asymmetry for σ Zh plays a very important role inthe EFT fit as explained in Sec. 4. The Higgs mass m h is also measured from the fit shown in Fig. 46. The esti-mate of m h uncertainty is 14 MeV for ILC250, with thedominant contribution from µ + µ − h channel. The uncer-tainty in the Higgs boson mass ( δm h ) does play a roleas a source of systematic error for predictions of Higgsboson couplings. In most cases, ∆ m h ∼
100 MeV wouldbe already sufficient, but this is not true for h → ZZ ∗ or h → W W ∗ . It has been pointed out in [118] that δ W = 6 . · δm h , δ Z = 7 . · δm h , (18)where δ W and δ Z are the relative errors for g ( hW W ) and g ( hZZ ) respectively. At ILC250, the 14 MeV accuracyfor Higgs boson mass results in systematic errors of 0.1%for δ W and δ Z . h → bb cc gg τ τ WW ∗ ZZ ∗ γγ γZ eff. [%] 88.25 88.35 87.98 88.43 88.33 88.52 88.21 87.64TABLE XIII: The efficiencies of the major SM Higgs decaymodes, after all the event selection cuts, shown here for thecase of the µ + µ − h channel and e − L e + R at √ s =250 GeV [185].The uncertainties due to finite MC statistics on these valuesare below 0.14%. As pointed out in the very beginning of this analysis,the key idea which enables the inclusive σ Zh measure-ment is that the signal is tagged independently of Higgsdecay modes. Hence it is crucial to examine whetherall the pre-selection and final-selection cuts satisfy thiscriterion. This can be verified by checking the signal effi-ciency for each individual Higgs decay mode and evaluat-ing the efficiency uniformity among all the decay modes.Table XIII lists the efficiencies of major SM Higgs de-cay modes after all cuts in the µ + µ − h channel. It isseen that there is no discrepancy in efficiencies of SMdecay modes beyond 1%. This is not a surprise becausethe analysis strategies and selection cuts are carefullydesigned to make it so. The cut E vis >
10 GeV maydeserve a few more words, since it apparently suppressesthe h → invisible mode. The strategy behind is that σ Zh can be measured as σ Zh = σ visZh + σ invZh , (19)where σ visZh is the total cross section for all h → visible modes, which is measured here, and σ invZh is the crosssection for h → invisible mode, which can be measuredseparately, described in Sec. 8.2.6. A detailed and quanti-tative analysis taking into account the possibility of exist-ing BSM decay modes is performed in [185]. It concludesthat the relative bias on σ Zh , induced by the Higgs de-cay modes dependence, can be controlled at below 0.1%7(0.2%) for the µ + µ − h ( e + e − h ) channel, which is muchsmaller than the expected statistical uncertainty even atthe full ILC250.In the hadronic recoil channel, a more complicatedstrategy is applied in order to keep the analysis still decaymodes independent. Instead of the simple categorizationinto visible and invisible modes in leptonic channel, thesignal events in hadronic channel are categorized accord-ing to number of taus, number of leptons, and numberof jets in the final state. In principle, as long as thecategories are inclusive, we can design and optimize theselection cuts category by category. The studies in [186]show that by varying the SM decay branching ratios by ±
5% (absolute) in each decay mode, the bias on mea-sured σ Zh is at most around 0.5% relatively. More effortswould be needed in future to further reduce the bias toa much lower level in particular even under assumptionthat there would be other unknown exotic decay modes.At higher √ s , the hadronic recoil analysis generally be-comes less challenging, because the two jets from primary Z are more boosted hence are easier to be identified fromthe Higgs decay products, as studied in [187, 188] for √ s = 350 and 500 GeV. σ ννh and σ eeh The second leading Higgs production process, e + e − → ννh via W -fusion, provides a direct measurement for hW W coupling. It plays a crucial role in the globalfit based on κ formalism, and still helps improve theglobal fit results based on EFT formalism even thoughthe cross section is not very large at √ s = 250 GeV, σ ννh = 14 fb for e − L e + R . The signal channel used is e + e − → ννh, h → bb , in which direct observable is σ ννh · BR bb . Together with BR bb measurement by Zh process, σ ννh is then measured. The analysis is briefly de-scribed here, and more details can be found in [189, 190].The signal final states consist of two b-jets and twomissing neutrinos. The pre-selection starts with veto-ing events with one or more isolated leptons. Thenjet-clustering and flavor tagging are performed with ex-pected number of jets equals 2. The two jets are requiredthat in each jet there are at least 6 reconstructed particlesand Y → < .
1, where Y → is the jet distance value from3 jets to 2 jets step defined by Durham algorithm. Theb-tagging of the two jets are required to be btag > . btag > .
2. The di-jet invariant mass is requiredto be m bb ∈ [110 , γZ ( Z → bb ), ννZ ( Z → bb ) and Zh ( Z → νν , h → bb ).In the final selection, γZ and ννZ background eventsare further highly suppressed by a BDT cut, which istrained using input variables di-jet mass, polar angle ofdi-jet, angle between two jets, and Y → . The remainingsignal and background events are plotted in the missingmass spectrum, shown in Fig. 48 (upper). The signal effi- Missing Mass [GeV]
40 60 80 100 120 140 160 E n t r i e s / G e V toy data H (fusion) νν signal H (ZH) νν M(H) / GeV
50 100 150 E n t r i e s vvh (WW fusion)vvh (ZH)4f_sznu_sl4f_zz_sl6f_yyvllvS + B H @ 500 GeV νν→ +e + e L = 500 fb ∫ ) = ( 0.8,+0.3) + ,e P(e
FIG. 48: Missing mass spectrum (upper) and Higgs massspectrum (lower) for the signal e + e − → ννh, h → bb and theSM background at 250 GeV and 500 GeV respectively[189, 190]. ciency is 36% and the average signal over background ra-tio is around 1/4. The most dominant background eventsturn out to come from Zh ( Z → νν ) and have significantoverlap with signal events in the missing mass spectrum.This is because the invariant mass of νν of signal eventscan not be far away from M Z , limited by available phasespace at √ s = 250 GeV. Therefore it is necessary to fitsimultaneously σ ννh · BR bb and σ Zh · BR bb . Note a usefulconstraint can be added into the fit that σ Zh · BR bb is alsomeasured using Z → l + l − and Z → qq channels. As aresult, the estimate of relative uncertainty on σ ννh · BR bb is 8.1%, shown in Tab. XI, and the correlation between σ ννh · BR bb and σ Zh · BR bb is -34%.The left-handed beam polarisation does help signifi-cantly the σ ννh measurement here, simply because it en-hances the cross section by a factor of 2.34. The σ ννh canbe measured much better at √ s = 500 GeV, shown in 48(lower), thanks to a fact of 10 increase on cross sectionand much easier separation with Zh ( Z → νν ).The third leading Higgs production process, e + e − → e + e − h via Z -fusion, is not easy to measure due to itsvery small cross section at √ s = 250 GeV, σ eeh = 0 . √ s = 250 GeVwith 2 ab − and σ eeh can be measured with a significance8 b l i k e n e s s c li k ene ss DataData b l i k e n e s s c li k ene ss others → h others → h b l i k e n e s s c li k ene ss SM BGSM BG b l i k e n e s s c li k ene ss bb → h bb → h b l i k e n e s s c li k ene ss cc → h cc → h b l i k e n e s s c li k ene ss gg → h gg → h FIG. 49: Template of b-likeliness versus c-likeness for signal h → bb/cc/gg (bottom left/middle/right) events, and for h → others / SM background (top middle/right) events, and distribution for all the events (top left), in Z → qq channelnormalized to 250 fb − . The b-likeness is defined as a combined function of the two b-tags (say x and x ) of the two jetsfrom h candidate: b − likeness = x x x x +(1 − x )(1 − x ) . The c-likeness is defined in a similar way. of 9 σ [180]. At √ s = 500 GeV, the significance will besignificantly improved to 60 σ . BR( h → bb/cc/gg )The capabilities of making precise measurements forBR( h → cc/gg ) demonstrate another unique advantageof a lepton collider, enabled by: (1) clear separation be-tween b-jets, c-jets and light quark/gluon jets thanks tothe excellent flavor tagging performance introduced inSec. 7; and (2) the democracy about cross sections be-tween Higgs processes and other SM background pro-cesses induced by electroweak interactions. The branch-ing ratios BR( h → bb/cc ) offer important measurementsof the Yukawa couplings between the Higgs boson andthird/second generation quarks. BR( h → gg ) offers adirect measurement of the hgg coupling, This is comple-mentary to that at the LHC, where this coupling is ob-tained from the Higgs production cross section, and hasmuch smaller theoretical uncertainties. These measure-ments are performed using the leading Higgs productionprocess e + e − → Zh . All the major Z decay channels Z → l + l − , Z → νν and Z → qq are used in the analyses;see details in Ref. [191].We now discuss in more detail the analysis procedurefor the Z → qq channel. The signal final states consist offour jets, common for h → bb/cc/gg . In the pre-selection,all the particles in each event are first clustered into fourjets using Durham algorithm. The four jets are pairedinto two di-jet pairs, j j and j j , as for respectively Z and h candidates by minimizing the χ defined as χ = ( m j j − M Z σ Z ) + ( m j j − M h σ h ) , where m j j ( m j j ) is the invariant mass of j j ( j j ),and σ Z (= 4 . σ h (= 4 . Z and h respectively de-termined using MC truth information. A cut χ <
10 isapplied. In the final-selection, to suppress the leptonic orsemi-leptonic background events, the number of chargedparticles in each jet is required to be >
4. To suppressthe qq background events, the jet clustering parameter Y → is required to be consistent with 4-jet characteristic,that log Y → > − .
7. In addition two cuts are appliedon the event thrust and thrust angle, that thrust < . | cos θ thrust | < .
9. The remaining background eventsare dominated by qqqq , mainly from hadronic decays of
W W and ZZ . A cut on the angle between j and j isapplied, 105 ◦ < θ j j < ◦ . A kinematic fitting is per-formed, using four-momentum conservation constraintsplus the constraint m j j − m j j = M Z − M h . Then,two cuts are applied on the fitted Z and h masses, that m j j ∈ [80 , m j j − M h ∈ [ − ,
10] GeV.As a final cut, a multivariate likelihood is derived andrequired to be Likelihood > . S/B ratio ofaround 1/10, including all events of h → bb/cc/gg (notethe S/B ratio for h → bb events is much higher).A template fit is then performed to extract the num-bers of signal events h → bb , h → cc and h → gg re-spectively, for which it is crucial that the different sig-nal events are distinguishable with themselves as well as9with background events. The templates are constructedas 3-D histograms using 3 variables, namely b-likeness,c-likeness and bc-likeness defined for the two jets j and j (as from h candidate). Five templates are made usingseparated MC samples: signal h → bb , h → cc , h → gg ,SM background and h → others background. The pro-jected 2-D templates for b-likeness versus c-likeness areshown in Fig. 49, each of which has been normalised to anintegrated luminosity of 250 fb − . It demonstrates thatthe three types of signal events can indeed be clearly dis-tinguished with themselves and with background events,thanks to the excellent flavor tagging performance andgood signal over background ratio.We just used Z → qq channel to illustrate the analy-sis, it is worth commenting that Z → νν channel is aspowerful as Z → qq channel despite its branching ratiois a factor of 3 smaller. This is largely due to the factorthat the signal and background discrimination in Z → qq channel is much degraded by performance of the realis-tic jet clustering and jet pairing algorithms at now, asa result of which the S/B ratio in Z → qq channel is afactor of 5 lower than that in Z → νν channel. Fromthe perspective of a better jet clustering or jet pairingalgorithm in future, the analysis in Z → qq channel canbe significantly improved.By combining Z → qq/νν/l + l − channels, the esti-mates of statistical uncertainties for σ Zh · BR bb , σ Zh · BR cc and σ Zh · BR gg are respectively 1.3%, 8.3% and 7.0%,shown in Table XI. BR( h → W W ∗ /ZZ ∗ )The measurements of branching ratios of h → W W ∗ /ZZ ∗ play an important role in the global fit asthe Higgs total width is determined byΓ h = Γ W W BR W W = Γ ZZ BR ZZ . Depending on how each
W/Z decays and how Higgs isproduced, there are quite many signal channels that canbe used. The analysis strategies as well as the signalbackground discrimination also vary quite a lot channelby channel. For Zh production and h → W W ∗ , the sig-nal channels are listed in Table XIV, where the channelswith marks are studied based on full simulation and en-ter the combined estimate of statistical uncertainty. Thedetails of event selections can be found in [192–194]. Oneof the dominant background processes in all channels is e + e − → W + W − , suppression of which can be helped bythe right-handed beam polarisations. Due to the multi-ple jets in the signal final states, the analysis could alsobenefit significantly from an improved jet clustering al-gorithm in future. The estimate of statistical uncertain-ties for σ Zh · BR W W is 4.6%, shown in Table XI. It’sworth noting from Table XIV that there are still manymore channels which yet to be employed in full simu-lation in future to improve the σ Zh · BR W W measure- h → / Z → l + l − νν qqW W ∗ → qqqq ∗∗ ∗ W W ∗ → qqlν ∗ W W ∗ → lνlν e + e − → Zh, h → W W ∗ and their branching ratios. The entries marked with * or **are currently studied by full simulation and enter thecombined result. The entry marked with ** is based onCEPC studies. M(H) / GeV
60 80 100 120 140 160 180 E n t r i e s vvh (WW fusion)vvh (ZH)4f_sznu_sl4f_sw_sl4f_ww_slS + B FIG. 50: Higgs mass spectrum for the signal e + e − → ννh, h → W W ∗ → qqqq and the SM backgroundevents, normalized to 500 fb − at 500 GeV [189]. ment, in particular the fully hadronic channel Z → qq and W W ∗ → qqqq that has the largest branch ratio.At √ s = 500 GeV, the BR ( h → W W ∗ ) measurementcan also be improved significantly by including Higgs pro-duction via W -fusion. Two signal channels e + e − → ννh , h → W W ∗ → qqqq/qqlν have been studied based on fullsimulation. As an illustration, the remained signal andbackground events in W W ∗ → qqqq channel after all cutsare plotted in Fig. 50 in the reconstructed h mass spec-tra. The signal peak can be clearly observed with thedominant background from ννh ( h → others ), ννZ and W + W − . The average S/B ratio is around 1 / . M ( h ) ∈ (114 , σ ννh · BR W W is 3.4% with 250 fb − at √ s = 500 GeV, shown in Table XI. It is worth notinghere the significant impact of overlay events. Figure 51shows the reconstructed h mass spectra for signal eventsin cases of no overlay, with overlay but using inclusiveDurham jet clustering algorithm, overlay removal usinganti- k T algorithm, and overlay removal using a new MVAbased algorithm; see details in [189]. It can be said thatthe performance of h mass reconstruction, in the realisticcase even with an optimized overlay removal algorithm todate, is still far away from the perfect case of no overlay.Therefore the σ ννh · BR W W measurement will benefit alot from a better overlay removal algorithm in future.For BR ( h → ZZ ∗ ) measurement, in general it is morechallenging due to its small branching ratio. Though0 Higgs Mass / GeV
50 100 150 200 N o r m a li z ed Durham (No Overlay)Durham (overlay)Anti kt (R = 1.2)MVA
FIG. 51: Higgs mass spectrum for the signal e + e − → ννh, h → W W ∗ → qqqq in different cases of overlay:no overlay (solid black) illustrating the performance ofperfect overlay removal; without overlay and withoutapplying any removal algorithm (dashed black); overlayremoval with traditional exclusive jet clustering algorithm,anti- k T here (blue); overlay removal with a new methodbased on MVA, optimized for this particular signal channel(red). The histograms are normalized to 500 fb − at √ s =500 GeV [189]. the analysis can be done similarly by combining analysesoptimized in many individual channels, a different strat-egy was used in [108]. All the signal events are selectedagainst background with a single multivariate method us-ing many variables as input. As a result, the estimate ofstatistical uncertainty for σ Zh · BR ZZ is 18%, shown inTab. XI. BR( h → τ + τ − )The measurement of BR ττ provides a very importantprobe of the Higgs couplings to third generation fermions.And it is going to be one of the most precise Higgsmeasurements at the ILC, thanks to the relatively largebranching ratio and very clean signal and backgroundseparation. The full simulation is performed using theleading Higgs production process e + e − → Zh and allthe decay channels from Z → qq/νν/l + l − ; see detailsin [195]. The τ is reconstructed using TaFinder andthe four momenta of missing neutrinos are calculated us-ing collinear approximation. The remained signal andbackground events in Z → qq channel are shown inFig. 52. The S/B ratio is higher than 2/1. The signalefficiency is 36% and the dominant background is from e + e − → ZZ → qqτ + τ − . The estimate of statistical un-certainty for σ Zh · BR ττ is 3.2%, shown in Table XI. BR( h → invisible / exotic)As introduced in 8.2.1, the recoil technique enables thatHiggs events can be tagged without looking into theHiggs decay products. This feature is extremely use- TMVA output
1 0.5 0 0.5 1 N u m be r o f e v en t s / .
10 signalbackground )=( 80%,+30%) + ,e ,P(e =250GeV,L=250fbsh,qq → e + e FIG. 52: MVA output for the signal e + e − → qqh, h → τ + τ − and the SM background at 250 GeV [195]. Recoil Mass [GeV]100 110 120 130 140 150 160 E v en t s / [ G e V ] ZZWWZ νν W ν e H νν qqH ν → qqH,Hinvisible BF 10% → H Simulation
ILD = 250 GeVs ) = (+0.8, 0.3) + ,e pol(e
250 fb
FIG. 53: Recoil mass spectrum against Z → qq for signalevents e + e − → Zh, h → invisible assuming BR ( h → invisible ) = 10% and SM background events at 250GeV for the right-handed beam polarisation [196]. ful for probing Higgs to invisible or other exotic decays.Full simulation studies are performed for e + e − → Zh , h → invisible using two signal channels Z → qq and Z → l + l − ; see details in [196–198]. The dominant con-tribution comes from Z → qq channel. After all thecuts, the recoil mass spectrum for the remaining sig-nal and background events is plotted in Fig. 53. Themain background events come from ZZ/ννZ → ννqq and W W → qqlν . The signal peak would be seen clearly forthe value BR ( h → invisible) = 10% assumed in the fig-ure. The actual sensitivity is much greater. We estimatethe 95% C.L. upper limit for BR ( h → invisible ) to be0.86% for the left-handed beam polarisations, as shownin Tab. XI. An upper limit factor of 1.5 lower can be ob-tained for the right-handed beam polarisations, thanksto the much reduced background level.Other exotic decays have not been studied based on fullsimulation. Nevertheless according to the fast simulationresults in Ref. [128], at ILC250 we would be able to probepartially visible exotic decays with branching ratios of10 − or below.1 BR( h → µ + µ − /γγ/γZ )The measurement of the SM rare decay branching ra-tios BR( h → µ + µ − /γγ/γZ ) are a bit challenging atthe ILC, mainly due to the limited number of signalevents. We expect significant contributions from HL-LHC for these measurements. Full simulations are per-formed in [199, 200], and the estimates of statistical un-certainties for σ Zh · BR µµ and σ Zh · BR γγ are respectively72% and 34%, shown in Table XI. BR ( h → γZ ) is alsostudied based on full simulation [201], a significance of2 σ would be expected with full ILC250. Higgs CP properties can be measured via the hτ τ cou-pling at the tree level,∆ L hττ = − κ τ y τ √ hτ + (cos Ψ CP + i sin Ψ CP γ ) τ − , (20)where the CP phase angle Ψ CP is determined using thetransverse spin correlation between the two τ , as shownin Fig. 54 (upper) in the ∆ φ (angle between transversespins of two τ ) distribution for different values of Ψ CP .The spin of each τ is estimated using the polarimeter vec-tor which can be fully reconstructed in some of τ decaymodes, such as τ → πν/ρν , taking advantage of precisemeasurements for impact parameters; see the method de-tail in [202]. Full simulation studies are performed usingsignal channels Z → qq/l + l − and h → τ + τ − in [203].Figure 54 shows the distribution of reconstructed ∆ φ for the remained signal and background events in oneof the golden event categories. The estimate of statis-tical uncertainties for CP phase angle is 4 . ◦ with fullILC250. Note that the Higgs CP violating effects canalso be probed in hZZ coupling using the ˜ b parametershown in next section. HV V cou-plings
The hZZ coupling can be deviated from SM not onlyin total strength but also in Lorentz structures, whichcan be detected by measuring differential cross sections.Full simulation studies are performed using e + e − → Zh events for measuring following effective hZZ couplings:∆ L hZZ = (1+ a ) m Z v hZ µ Z µ + 12 bv hZ µν Z µν + 12 ˜ bv hZ µν ˜ Z µν , (21)where the first a -term is a rescaling of SM hZZ cou-pling, the second b -term and the third ˜ b -term representrespectively anomalous CP-even and CP-odd hZZ cou-plings. The total cross section σ Zh is sensitive to both a and b parameters, but b is distinguished from a in thedifferential cross sections; see Fig. 55 (upper) how Z pro-duction angle depends on values of b . σ Zh depends on ˜ b rather weakly, only quadratically. But the angle between [rad] φ ∆ − a r b i t r a r y no r m a li s a t i on =0 CP ψ /8 π = CP ψ /4 π = CP ψ /2 π = CP ψ /4 π =3 CP ψ [rad] φ ∆ − − − / r ad ) π e v en t s / ( χ Group A/nDOF= 29.3/19 χ − ab , 0.9 + R e − L eILD simulation: 250 GeV, qq → Z FIG. 54: Upper: ∆ φ distributions at MC Truth level fordifferent values of Ψ CP for the signal e + e − → qqh, h → τ + τ − at 250 GeV; Lower: reconstructed∆ φ distributions after all cuts in the dominant category forthe SM signal (in red) and the SM background (blue)respectively [203]. Zh production plane and Z decay plane, namely ∆Φ, isvery sensitive to ˜ b ; see Fig. 55 (lower) for ∆Φ distribu-tions for different values of ˜ b . The analysis details canbe found in [204]. The estimate of statistical uncertain-ties for a and b are 0.076 and 0.027 respectively, with alarge correlation ρ = − . √ s = 500 GeV, as shown in Fig. 56, becausethe effect of b -term is momentum dependent. The CP vi-olating parameter ˜ b can be determined with a statisticaluncertainty of 0.004 for the full ILC250, with almost nocorrelation with a or b . For the studies of the Higgs boson in which we wishto claim that precisely measured deviations from theSM can give a discovery of new physics, we must becertain that systematic errors are both small and well-constrained. In this section, we will discuss the sourcesof systematic error that we consider in our Higgs couplinganalysis.We will also discuss the capability that the ILC givesto control systematic uncertainties using the availability2 Z θ cos
1 0.5 0 0.5 1 Z θ / d c o s σ d σ / × Z impact of b = 1 Z b = 0 Z b =+1 Z b =+1 w/o SM Z b H @ 250GeV µµ→ + e e )=( 100%,+100%) + ,e P(eProduction angle in the Lab. frame planef(Z)f Φ∆ p l a n e f( Z )f Φ ∆ / d σ d σ / × Z b~impact of = 1 Z b~ = 0 Z b~ =+1 Z b~ =+1 w/o SM Z b~ H @ 250GeV µµ→ + e e )=( 100%,+100%) + ,e P(eIn the Lab. frame
FIG. 55: Upper (lower): cos θ Z (∆Φ) distributions at MCTruth level for different values of anomalous coupling b (˜ b )for the signal e + e − → µ + µ − h, h → everthing at 250 GeV;[204]. of polarized beams. In precision measurement, it is use-ful, wherever possible, to measure effects correlated tosources of systematic uncertainty. For this, it is crucialto always have one more degree of freedom that (statisti-cally) absolutely required. In the ILC program, electronand positron polarisation provide tools to validate esti-mates of systematic errors, and to reduce these sourcesof uncertainty. In Sec. 4.10, when we reviewed in generalterms the importance of the use of beam polarisation tomeet the physics goals of the ILC, we did not empha-size this aspect of the physics implication of polarisation.But it is clear that, for each measurement that can bedone at an unpolarized collider, a collider with control ofthe polarization for each beam can provide four indepen-dent data sets. We will explain in this section how thistool can be used not only to estimate but also to reducesystematic errors. The evaluation of systematic uncertainties for experi-ments which have not yet been built is a difficult taskand will to some extent always remain guess-work un-til real data have been taken. To some extent, we canrely on the experience from previous e + e − experiments,especially at LEP, where many uncertainties could becontrolled to a typical level of 1%. The ILC detector de-signs, which aim for higher precision, make use of thisexperience, as explained in Sec. 6. Assuming this basiclevel of performance, detailed studies of systematic un-certainties at the ILC have concentrated on cases wherethe statistical uncertainties are expected to be signifi-cantly below 1%, and on searches in channels with largeirreducible backgrounds. An example for the first caseis a global analysis of total rates and differential distri-butions of various 2-fermion and 4-fermion SM processes,extracting simultaneously the total unpolarised cross sec-tions, the relevant left-right asymmetries, the beam po-larisations and the charged triple gauge couplings, seeSec. 9.1 and Ref. [109]. An illustrative example for thesecond category, though not directly connected to Higgsphysics, is the WIMP search in the mono-photon chan-nel, see Sec. 12.2 and Ref. [106].Studies of this type lead us to the following estimatesof the dominant systematic uncertainties. These sourcesof systematic uncertainty are also applied to the mea-surements of triple gauge boson couplings described inSec. 9.1. • The luminosity at the ILC will be measured fromlow-angle Bhabha scattering with the help of adedicated forward calorimeters, the LumiCals (seeSec. 6.2.5 and Ref. [205]). This measurement isextremely sensitive to the exact alignment of theLumiCals on the two sides of the detector, aswell as to beam backgrounds and has been stud-ied in detailed simulations both for the ILC andfor CLIC [206, 207]. Based on these studies, theresulting systematic uncertainty on all Higgs crosssection and cross-section-times-braching-ratio mea-surements is assumed to be 0.1% • Another 0.1% is assumed for the net systematic ef-fect of the finite knowledge of luminosity-weightedlong-term average values of the beam polarisationsat the e + e − interaction point. Compton polarime-ters in the Beam Delivery System will provide time-stable measurements of the beam polarisations attheir locations at the level of 0.25% [95, 208]. Toobtain the polarisations relevant for the experi-ments, one must also consider also the effects ofspin transport, misalignment of beam line mag-nets as well as depolarisation during the beam-beam interaction [209]. The absolute scale of theluminosity-weighted average polarisation at the IPis finally calibrated from collision data, e.g. , from a3 FIG. 56: 68% and 95% C.L. contour plots for fitted parameter a versus b at 250 GeV (left) and 500 GeV (right) [204]. global fit to SM processes with strong polarisationdependence [109]. • Theoretical uncertainties are also assumed to havereached the level of 0.1% by the time of ILC op-eration. This requires the computation of all rele-vant processes to 2 loops in the electroweak inter-actions, a task feasible within the current state ofthe art [210]. Another question is the availability ofhigh-precision values for the most important inputparameters— m b , m c , α s , and m h . We expect toobtain the first three of these to sufficient accuracyfrom lattice QCD [118]. For m h , the ILC recoilmeasurement described in Sec. 8.2.1 will providethe high precision needed. • For flavor tagging, systematic errors of 1% havealready been reached at LEP. With the advancesin detector technology and the larger integratedluminosity, we assume that for each data set atthe ILC this can be reduced and also improved asa function of integrated luminosity by probe-and-tag measurements. We expect an uncertainty of0 . (cid:112) . /L , where L is the integrated luminos-ity in ab − . This is an error of 0.1% for the ILC250. In the remainder of this section we will highlight the im-pact of the beam polarisation on the control of systematicuncertainties using these two studies as examples. Wehave already pointed out that beam polarisation providessubsets of the data that can be used as cross-checks ofsystematic errors on efficiencies for signal identificationand background suppression. However, the studies inRefs. [106] and [109] go beyond this to illustrate the use of beam polarisation to actually reduce systematicerrors beyond what is possible at an unpolarised collider.Both of these studies were carried out for measurementsat the 500 GeV ILC, but the same principles apply tothe 250 GeV data.Several principles combine to produce this result. Thefirst is that different polarization settings produce eventsamples with different mixtures of signal and backgroundprocesses. The differences in these mixtures arise fromorder-1 polarization asymmetries that vary from processto process, to first approximation, in the manner pre-dicted by the SM. In the SM, for example, lepton pairproduction has a small polarization asymmetry while thepolarization asymmetry for bb production is large andthat for W pair production is almost maximal. For cer-tain modes, for example, lepton pair production and di-jet production, the detection efficiency is naturally veryhigh and therefore has a small uncertainty, while for otherprocesses, for example, bb production, this efficiency issmaller and also more complicated to estimate. If weintroduce nuisance factors for the more uncertain effi-ciencies and determine these from data, the correlationof the relative compositions with polarization allows usto determine these parameters in terms of the efficienciesthat are better known.The second principle is that systematic uncertaintiesthat are correlated with polarization can be cancelledlocally in the data set using fast reversal of the beam he-licities. This principle was essential to the excellent mea-surement of sin θ w by the SLD experiment from a verysmall data sets; almost all systematic errors were can-celled by flipping the e − beam polarization in a pseudo-random fashion [211]. The principle of rapid helicity re-versal is built into the ILC design, which gives the ca-pability to flip the sign of polarisation for each of thetwo beams independently on a train-by-train basis (see4 l q + W aD l q - W aD l q WW aD l q ZZ aD qq Z aD ll Z aD - - - - = 1% p / pD = 1%; e / eD statistical error only systematics correlated (cid:222) polarized systematics uncorrelated (cid:222) unpolarized = 1% p / pD = 1%; e / eD FIG. 57: Uncertainties on the unpolarised cross sections ofvarious 2-fermion and 4-fermion processes as obtained fromthe global fit introduced in the text [109], assuming asystematic uncertainty of 1% on the selection efficiencies andpurities, each. In the case of polarised beams, it is estimatedthat only 10% of the uncertainty is uncorrelated betweendata sets. Applying that estimate to the analysis of data setstaken “quasi-concurrently”, the impact of the systematicuncertainties is minimal. Without the redundancies providedby data sets with correlated systematic uncertainties, thetotal uncertainties increase by a factor 2 for
W W andsingle- W processes and a factor of 5 for 2-fermion processes. Sec. 2.3.1. This helicity reversal is fast compared to typ-ical time-scales of changes in the configuration, calibra-tion, and alignment of the detector and the accelerator.It implies that data sets with the same beam energy butdifferent beam helicities can be considered as being col-lected essentially concurrently.The improvement in the measurement of the absolutenormalization of cross sections can be very significant.The study of Ref. [109] considered the full set of 2-fermionproduction processes and 4-fermion production processes(including e + e − → W W/ZZ → W production) at 250 GeV. Each channel was as-signed a 1% systematic uncertainty in its selection effi-ciency and signal purity. Based on the correlations ofexperimental effects between “quasi-concurrently” takendata sets, discussed in section 8.3.2, it was estimatedthat only 10% of this uncertainty is uncorrelated betweendata sets with different beam polarisation configurations.Thus, a global fit using all four polarization settings al-lows one to determine the relative efficiencies and removemost of the systematic uncertainty. The result for the fi-nal normalization uncertainties are shown in Fig. 57. Foreach of several 2- and 4-fermion channels, the black barsshow the statistical uncertainties, the red bars show thefull uncertainties for unpolarised data, and the blue barsshow the uncertainties for polarised data samples. Thefinal uncertainties are larger in unpolarized case by a fac-tor of 2 for W W and single- W processes and by a factorof 5 for lepton pair production.The same principles can be applied to the measure-ment of polarisation asymmetries A LR , which, as we have ) q q n ( e + W bD ) q q n ( e - W bD ) qqq ( q WW bD ) q q n ( l WW bD ) q ( q Z bD ) - l + ( l Z bD - - - -1 fi + e - GlobalFit: e – – )= + ,e - P(e 80%, 0 – )= + ,e - P(e -1 fi + e - GlobalFit: e
FIG. 58: Uncertainties ∆ β on A LR of various 2-fermion and4-fermion processes as obtained from the global fitintroduced in the text [109] with both beams polarised (withthe standard 45%/45%/5%/5% sharing between the fourhelicity configurations) and in the absence of positronpolarisation (with a 50%/50% sharing between the tworemaining helicity configurations). In the absence ofpositron polarisation, the uncertainties on A LR increase by afactor 2 for W W and by about a factor of 10 for 2-fermionprocesses. Alone the single- W processes remain unaffected. seen, play a large role in the ILC program. Though manysystematic errors automatically cancel in A LR , there arenew sources of systematic uncertainty, for example, thepossibility of a correlation between the helicity orienta-tion and the luminosity delivered per bunch train. Thisis effectively controlled if both the electron and positronbunches can be polarised. Roughly, the polarizationasymmetry in W pair production is almost maximal, andthe small uncertainty in this quantity can be transferredto the value of A LR for other processes. The point isillustrated in Fig. 58, again from Ref. [109], which showsa comparison of the final uncertainty on A LR in a globalfit between a collider with e − and e + polarization (blackbars) and a collider with only e − polarization (red bars).The improvement is a factor of 10 for fermion pair pro-duction. (In this illustrative study, the systematic errorsfrom detector efficiency and theory are set equal to zero.)Similar large effects from polarisation are seen in casesin which the signal is detected in the shape of a dis-tribution. An illustration here is given by a study ofthe search for dark matter particles χ using the mono-photon signature [106], already discussed in Sec. 4.10. Inour earlier discussion, we pointed out that the signal from e + e − → γχχ sits on top of a large irreducible backgroundfrom e + e − → γνν . The study includes a careful evalu-ation of the systematic uncertainties, including those onselection efficiencies, luminosity, beam energy (spectrum)and polarization as well as on the theoretical modellingof the background. The limit calculation uses fractionalevent counting based on the observed energy spectrumof the selected photon candidates and considers normal-isation and shape-dependent uncertainties as well as the5 [GeV] c M
50 100 150 200 250 [ G e V ] L EFT not validILDVector, 500GeV
With syst. uncertainties, H20 pol. mix. -1 + ,e _ , P(e -1 + ,e _ , P(e -1 -1 e xc l u s i on r eg i one x pe c t ed W I M P FIG. 59: Comparison of the reach of the search for WIMPproduction in the mono-photon channel for differentassumptions on luminosity and polarization, including systematic uncertainties (see Sec. 12 for a description of theanalysis) [106]. correlations between these. If the mass of the χ is rel-atively high, only low-energy photons can appear in thesignal process. Then the high-energy part of the photonspectrum can be used to determine nuisance parametersassigned to the polarization and efficiencies. The resultsfor the lower limit on the mediator scale, including sys-tematic errors, are shown in Fig. 59. This figure shouldbe compared to Fig. 25, in which systematic errors areset to zero. Note that, in this case, the strongest limitsare set using a mixture of beam polarizations (the dashedred curve in both cases) since this allows the systematicerrors from beam polarisation to be better controlled. As elaborated in the previous section, all the estimatesfor Higgs measurements shown in Tab. XI are based onavailable full simulation studies, which are performed us-ing the analysis techniques known at present. These es-timates are clearly too conservative in the sense that wehave not been able to analyse all useful signal channels.In addition, analysts working closely with the data arealways able to invent algorithms to that are more clev-erly optimized to the data that is actually collected. Theprojected uncertainties quoted here and in Sec. 11.1 donot take advantage of these likely improvements.Since the formal estimates of the performance of HL-LHC given in the HL-LHC Yellow Report [126] do takeinto account improvements in systematic uncertaintiesthat are anticipated but not yet realised, it seems to usreasonable to define also for ILC an optimistic scenariowith improved performance. We use this scenario to com-pare to the results of Ref. [126] in the manner explainedin Sec. 11.3. This scenario, which we refer to as “S2” inthat discussion, includes the following improvements inthe analysis just described. In all cases, these improve- ments are under study using our full simulation tools andare suggested, if not yet validated, by our current results: •
10% improvement in signal efficiency of the jet clus-tering algorithm. •
20% improvement in the performance of the flavortagging algorithm. •
20% improvement in statistics by including moresignal channels in σ Zh · BR ( h → W W ∗ ). • a factor of 10 improvement in the precision elec-troweak input A (cid:96) thorugh the measurment of e + e − → γZ with polarized beams at 250 GeV. •
30% improvement in the precision of Higgs self-coupling and top-Yukawa coupling at 500 GeV,which is a consequence of the improvements in jetclustering algorithm, flavor tagging algorithms andstatistics by including more signal channels.
The trilinear Higgs coupling can be measured at col-liders in two different ways. First, the coupling can bemeasured directly, using processes with Higgs pair pro-duction that diagrams involve the triple Higgs couplingat the tree level. Second, the coupling can be measuredindirectly, since radiative corrections to single-Higgs pro-cesses can include effects due to the tripple Higgs cou-pling.The important Higgs pair production reactions at e + e − colliders are e + e − → ZHH and e + e − → ννHH ,shown in Fig. 60. Note in both reactions there are dia-grams that do not involve trilinear Higgs coupling. Thefirst of these processes can be studied already at 500 GeV;the second, which is a 4-body process, requires somewhathigher energy. The cross sections of these two processesas a function of √ s are shown in Fig. 61. Full simulationstudies at a √ s =500 GeV show that a discovery of thedouble Higgs-strahlung process is possible within the H20program, using Z → l + l − /νν/qq and hh → bbbb/bbW W ∗ channels. With 4 ab − at 500 GeV, a combination ofthose decay channels would yield a precision of 16.8%on the total cross section for e + e − → ZHH [212–214].Assuming the SM with only the trilinear Higgs couplingfree, this corresponds to an uncertainty of 27% on thatcoupling.At still higher energy vector boson fusion becomes thedominant production channel. Making use of this chan-nel, with 8 ab − at 1 TeV, the studies of Refs. [213–215]show that, in the same context of varying the trilinearHiggs coupling only, this coupling can be determined to10%.The impact of the center-of-mass energies on the tri-linear Higgs coupling measurement is studied by extrap-olating the full simulation results done at 500 GeV and1 TeV to other energies. Due to the existence of dia-grams that do not involve the trilinear Higgs coupling in6 ZHZ HH e + e − ZHZ H e + e − ZHZ H e + e − ZHZ H e + e − + + +Background diagramsSignal diagram(a) + + +Background diagramsSignal diagram(b) HHH νν − e + e − HH νν − e + e − HH ν ν − e + e − HH ν e + e − ν − FIG. 60: Diagrams contributing to (a) e + e − → Zhh and (b) e + e − → ννhh . Center of Mass Energy / GeV
400 600 800 1000 1200 1400 C r o ss S e c t i on / f b ZHH → - + e + e HH (WW-fusion) νν → - + e + e HH (Combined) νν → - + e + e ) = (-0.8,+0.3) + ,e - M(H) = 125 GeV P(e
FIG. 61: Cross sections for the double Higgs productionprocesses, e + e − → Zhh and e + e − → ννhh , as a function of √ s for m h = 125 GeV. both reactions, to get the correct extrapolation a carefulanalysis taking into account the dependence on √ s forboth the total cross sections and interference contribu-tions was performed in Ref. [216]. The results are shownin Fig. 62 as the blue lines for the two reactions. In ad-dition to the results from realistic full simulations, theexpectations for the ideal case, assuming no backgroundand 100% signal efficiency, are shown as the red linesin the figure. The differences between the blue and theread lines, is as large as a factor of 4-5. This suggeststhat there is much room for improvement in the clus-tering algorithm used to identify 2-jet systems with theHiggs boson mass, which lead to improvements in the fi-nal results. Improvements could also come from betterflavor-tagging algorithms and inclusion of additional sig-nal channels such as Z → τ + τ − . The figure does implythat √ s = 500–600 GeV is optimal for e + e − → Zhh butthat CM energies of 1 TeV or above would be needed for e + e − → ννhh . Since large deviations of the trilinear Higgs couplingare expected in some new physics models, in particularin models of electroweak baryogenesis, it is interestingto see how the expected precisions would change in thatcase. Figure 63(left) gives the cross sections of the two re-actions as a function of the actual triple Higgs coupling λ ,and Figure 63(right) shows the expected precisions of theILC measurements. The natures of interference betweenthe triple Higgs coupling and the SM production am-plitude is very different for the two reactions, construc-tive for e + e − → Zhh but destructive for e + e − → ννhh .Therefore, the two reactions, useful at 500 GeV and 1TeV respectively, are complementary in determining thetrilinear Higgs coupling. If the trilinear Higgs coupling isindeed a factor of 2 larger, as expected in some models,the double Higgsstrahlung process at 500 GeV becomesvery useful and would already provide a measurement ofaround 15% precision for the trilinear Higgs coupling.The indirect determination of the trilinear Higgs cou-pling is based on the observation of McCullough [217]that the cross section for e + e − → ZH contains a ra-diative correction involving the trilinear coupling thatlower the cross section by about 1.5% from 250 GeV to500 GeV, with most of the decrease taking place below350 GeV. Taken a face value in the simple context withonly the trilinear coupling free, the ILC cross sectionmeasurements would determine the trilinear coupling toabout 40%.It is important to note, however, that the determina-tion of the trilinear coupling involves two separate ques-tions. First, is the SM violated? The accuracies withwhich this question can be answered are those givenabove. Second, can the violation of the SM be attributedto a change in the trilinear coupling or the Higgs poten-tial rather than being due to other possible new physicseffects? A precise way to ask this question is: Can theshift of the trilinear coupling be measured independently7 [GeV]s
500 1000 1500 2000 2500 3000 [ % ] λ / λ δ ZHH (100% Eff., no Bkg.) → +e + e ZHH (full simulation) → +e + e [GeV]s
500 1000 1500 2000 2500 3000 [ % ] λ / λ δ HH (100% Eff., no Bkg.) νν→ +e + e HH (full simulation) νν→ +e + e FIG. 62: The expected precisions of λ as a function of √ s for e + e − → Zhh (left) and for e + e − → ννhh (right). The twolines in each plot correspond to ideal situation (red) and realistic situation (blue) as described in the text. Same integratedluminosities of 4 ab − is assumed at all √ s . SM λ / λ S M σ / σ → +e + e HH @ 1 TeV νν→ +e + e SM λ / λ [ % ] λ / λ δ ZHH @ 500 GeV → +e + e HH @ 1 TeV νν→ +e + e FIG. 63: Left: the cross section as a function of λ for e + e − → Zhh (red line) and for e + e − → ννhh (blue line), where valuesof both λ and σ are scaled to their SM values. Right: expected precisions of λ when λ is deviated from its SM value. of possible effects of all other dimension-6 EFT opera-tors? To our knowledge, this latter question has onlybeen addressed for determinations of the trilinear cou-pling at lepton colliders. In Ref. [218] it is shown that,after the ILC H20 program of single-Higgs measurementsis complete, the uncertainty in the measurement of thetotal cross section for e + e − → ZHH receives a negligi-ble 2.5% uncertainty due to variation of the other rele-vant dimension-6 EFT perturbations. In Ref. [219], it isshown that, when the cross section for e + e − → ZH is fittogether with other relevant observables at 250 GeV and500 GeV, the uncertainty in the coupling is not substan-tially changed from the value of 40%. This conclusion,however, might be sensitive to the precision of the inputsfrom precision electroweak observables. A study of thoseeffects is in progress.
9. PHYSICS SIMULATIONS: ELEC-TROWEAK PRODUCTION OF 2- AND4-FERMION FINAL STATES
The precision studies of the Higgs boson described inthe previous section receive important and complemen-tary support from analyses of 2- and 4-fermion final stateswhich do not directly involve Higgs bosons, but our well-known SM gauge bosons — or potentially their yet tobe discovered siblings. In this section, some of the keyexamples introduced in Sec. 4.7 will be discussed in moredetail, highlighting the level of realism on which the pro-jections are based. e + e − → W + W − The analysis of four-fermion processes, e.g. from W -pair production, but also Z -boson pairs and single-bosonprocesses, plays a key role in the ILC physics program.As discussed in Sec. 4.7, constraints on triple gauge cou-plings (TGCs) are an important input to the dim-6 EFT-based interpretation of Higgs precision measurements in-8troduced in Sec. 4.6. Prospects for this type of analysishave been intensely studied in full detector simulation(c.f. Sec. 7), however only at center-of-mass energies ofat least 500 GeV. In this section, we will start out bysummarizing these detailed studies, and then proceed totheir recent extrapolations to a center-of-mass energy of250 GeV. The prospects for probing charged TGCs at the ILChave been studied in full, GEANT4-based simulationof the ILD detector concept at √ s =500 GeV [220] inthe context of the ILD Letter of Intent [155] and at √ s =1 TeV [221] as a benchmark for the ILD DetailedBaseline Design (Vol 4 ILC TDR [5]). Both analy-ses focused on the channel e + e − → W + W − → qqlν , l = e, µ and followed a similar, cut-based selection ap-proach. Thereby they exploit the known initial state fora full kinematic reconstruction of both W bosons, un-der consideration of optional photon radiation collinearto the beam direction. Neither the case l = τ , nor thefully hadronic mode, nor contributions from single- W production were included at the time. Especially the fullyhadronic mode will profit substantially from the recentadvances in reconstructing the jet charge with the ILDdetector, c.f. Sec. 9.2, in order to determine the chargesof the W boson candidates.Figure 64 shows one of the final observables sensitiveto anomalous TGCs, namely the cosine of the polar an-gle of the W − boson, cos θ W , which is reconstructed fromthe hadronically decaying W boson. The left part of thefigure illustrates the high purity of the selection whichranges between 85% and 95%, depending on whether W W → qqτ ν is considered as background or not. Theright panel shows relative deviation of the reconstructedcos θ W from MC truth, indicating a resolution of betterthan 0.5%.In the 500 GeV analysis, no pile-up from γγ → low p t hadrons was considered, which has, at √ s =500 GeV, anexpectation value of 1.2 events per bunch crossing, c.f.Sec. 7. This type of background was considered, how-ever, in the TGC study at 1 TeV, where its expectationvalue increases to 4.1 pile-up events per bunch cross-ing. Figure 65 shows the impact of these pile-up eventson the reconstructed hadronic W -boson mass without(“Durham”) and with (“Kt”) application of suitable sup-pression algorithms (see Sec 8.1 for a detailed descriptionof the algorithm). It can be seen that the residual ef-fect is small even at 1 TeV, where the number of pile-upevents is expected to be nearly four times higher than at500 GeV.Both full-simulation studies used only three out of fivepossible angular distributions which could provide sen-sitivity to TGCs: besides the production angle of the W − , the two angles describing the direction of the decaylepton in the restframe of its mother W were consid-ered in a five-parameter fit based on MC templates. The free parameters of the fit were the three TGCs g Z , κ γ and λ γ as well as the absolute values of the electron andpositron beam polarisations. With this approach, statis-tical uncertainties of about 6-7 · − were obtained for allthree couplings for an integrated luminosity of 500 fb − at √ s =500 GeV, shared equally between all four beam po-larisation configurations. In the context of the 500 GeVanalysis a thorough evaluation of the systematic errorswas performed. It was found at the time that uncertain-ties on the selection efficiencies of signal and backgroundof 0.2% and 1%, respectively, would lead to systematiceffects in the same order of magnitude as the statisticaluncertainty for 500 fb − .A recent study dedicated to a global fit of total anddifferential cross sections of various SM processes sensi-tive to TGCs and/or beam polarisation has shown, how-ever, that a much better control of systematic effectscan be achieved — provided that both beams are po-larised [109, 110].The full simulation study at √ s =1 TeV, following thesame fitting approach, found statistical uncertainties ofabout 2-3 · − for all three TGCs for an integrated lu-minosity of 1000 fb − . The effect of different sharings ofthe luminosity between the four polarisation sign combi-nations on the TGC precisions were found to be minor. While extensive studies of
W W production exist athigher center-of-mass energies, no complete analysisbased on full detector simulation is available yet for √ s =250 GeV. Nevertheless substantial progress hasbeen made in various important aspects which have beenincorporated in an extrapolation [4] based on a) the pre-viously discussed full-simulation studies at 500 GeV [220]and 1 TeV [221] and b) the actual LEP results at ∼
200 GeV [222]: • As discussed in Sec. 4.7, the sensitivity of measuredcross sections to the TGCs depends on the center-of-mass energy as s/m W . • Naively, the statistical uncertainties on measuredcross sections scale as 1 / √ σ L . However at highercenter-of-mass energies, the W bosons are moreand more boosted into the forward direction dueto increasing amount of ISR and beamstrahlung.Therefore the experimental acceptance decreasesfor higher √ s . A correction factor for this effecthas been derived [223] from a comparison of the fulldetector simulation studies at 500 GeV and 1 TeV. • The dependence on the sharing of luminosity be-tween the four different polarisation configurationswas found minor [221] and therefore no correctionsfor differences in the assumptions of the full simu-ation studies w.r.t. the H20 running scenario (c.f.Sec. 3.2) were applied.9 W θ cos
1 0.5 0 0.5 1 n e v en t s SignalTau signalqq4 ferm6 ferm γγ TW θ )/cos TW θ cos W θ (cos n e v en t s FIG. 64: Left: Reconstructed polar angle distribution cos θ W of the W − boson candidates for signal and SM backgroundevents before the application of the final selection cut cos θ W > -0.95. Right: relative deviation of the reconstructed cos θ W from the MC truth value cos θ T W . Both from [220]. (GeV) W m n e v en t s bkg. γγ no -> had., Durham γγ -> had., Kt R = 1.3 γγ FIG. 65: Reconstructed mass of the hadronically decaying W boson at √ s =1 TeV without pile-up compared to thesituation with pile-up in absence (“Durham”) or presence(“Kt”) of a mitigation strategy in the analysis. From [221]. • The improved treatment of systematic uncertain-ties based on a nuisance parameter technique ina global fit to many observables and datasets ex-plored in [109] was assumed, which leads to a con-stant ratio between systematic and statistical un-certainties up to luminosities of at least 2 ab − . • The full simulation studies were found to be lim-ited their MC-based, binned fit of 3D-template his-tograms. The relative improvement expected whenincluding the fully hadronic channel and when ex-ploiting all five sensitive angles (production angleof one of the W bosons plus decay angles of both W bosons, see e.g. Fig. 5.16 in [220] for an ilustration)in an unbinned fit [224], or, equivalently, when ap-plying an optimal observable technique [225, 226],was estimated in a parton-level study to be a fac-tor 2.4 in the case of g Z , and a factor of 1.9 for the other two couplings. • Since none of the ILC full-simulation studies evalu-ated the precisions for single-coupling fits, i.e. whenfixing the other two anomalous couplings to 0 asdone in hadron collider studies, the correspond-ing LEP2 results [222] were extrapolated up incenter-of-mass energy, and then the minimum ofthis extrapolation and of the 3-coupling extrapola-tion from ILC studies was taken.The results of this procedure are displayed in Tab. XVand Figs 66 and 67 in comparison with the LEP2 andLHC results as well as HL-LHC projections, where appli-cable. In case of the single-parameter fits, the 250 GeVstage of the ILC will improve the precision on g Z and κ γ by factors of 5 and 30 w.r.t to HL-LHC, while theprojections for λ γ are comparable. The loss in precisionwhen fitting all three couplings simultaneously to ILCdata is minor, and the resulting precisions are used asinput for the EFT-based Higgs coupling fit discussed inSec. 11.1. Actually, it has been shown it is possible evento determine simultaneously the 14 complex couplingsin the most general parametrisation of triple gauge bo-son vertices, including e.g. CP violating contributions,at e + e − linear colliders when both beams are polarisedand all polarisation configurations, including transversepolarisation, are exploited [226]. W mass measurement at 250 GeV The analysis of W + W − → qqlν discussed in the previoussections, as well as the study of single- W events also offeran excellent setting for the measurement of the W mass.As discussed in Sec. 4.8, the available statistics at the250 GeV ILC will be about a factor of 2000 larger thanat LEP2, which makes it obvious that a pure consider-ation of statistical uncertainties is meaningless. While0 total error ( × − ) correlationExp N par g Z κ γ λ γ g Z κ γ g Z λ γ κ γ λ γ LEP 2 3 516 618 376 -0.17 -0.62 -0.15ILC 250 3 4 . . . . . . √ s = 250 GeV with 2000 fb − luminosity (ILC 250). The LEP 2 result is fromALEPH [222] at √ s ≈
200 GeV with 0.68 fb − . The LHCresult is from ATLAS[227] at √ s = 7 TeV with 4.6 fb − .The HL-LHC estimate is from a 2013 overview of HL-LHCphysics [228]. From [4]. TGC Limits @ 68% CL0.05 - g lD g kD g D LEP2 ATLAS CMS HL-LHC ILC 250
FIG. 66: Comparison of the reachable TGC precision fromsingle parameter fits: ILC [229], final results from LEPcombined from ALEPH, L3 and OPAL results [230] and theLHC TGC limits for √ s = 8 TeV data and an integratedluminosity of L = 20 . − and L = 19 . − for ATLASand CMS, respectively [231]. TGC Limits @ 68% CL0.05 - g lD g kD g D LEP2 ILC 250
FIG. 67: Comparison of the reachable TGC precision from asimultaneous fit of all three parameters: ILC [229] and finalresults from LEP combined from ALEPH, L3 and OPALresults [230]. No comparable hadron collider results areavailable. the studies discussed in Sec. 9.1.1 showed that this kindof events can be selected with high efficiency and pu-rity, a careful extrapolation of the systematic uncertain-ties of previous measurements is therefore much moreinstructive than the evaluation of the statistical uncer-tainty from full detector simulation. Apart from a scan ofthe production threshold, kinematic reconstruction of W pair events and calorimetric comparison of hadronic W and Z decays in single-boson events are the most promis-ing techniques, which are described in detail in [232, 233].With a combination of methods and considering advancesin theory as well as in the performance of the detectorsthe systematic limit has been estimated as 2.4 MeV. Thisis expected to be reached already at the 250 GeV stageof the ILC. Additional datasets at higher center-of-massenergies could then provide independent information inorder to cross-check and constrain systematic effects. e + e − → f f Another important class of processes at e + e − collid-ers is fermion-antifermion production, which is highlysensitive to various new physics models, as discussed inSec. 4.8. Thereby, the important observables are thepolarised total cross sections, in particular in form ofthe left-right asymmetry A LR , as well as the differentialcross section as a function of the polar angle, dσ/d cos θ ,which contains even more information than the forward-backward asymmetry A FB . At center-of-mass energies above the Z pole, di-fermionproduction will be accompanied frequently by a signif-icant amounts of ISR. For example, at √ s =250 GeV,about half of the di-fermion events return to the Z pole.The ISR photons may escape undetected through thebeam pipe, or they can be produced at a sufficiently largeangle to be measured in the detector. The forward ac-ceptance of the ILC detectors is assisted by dedicatedforward calorimeters described in Sec. 6.2.5.In the latter case, energy and momentum constraintscan be employed to reconstruct the full event kinematicsfrom the angles of the fermions and the photon, withoutrelying on their calorimetrically measured energies or mo-menta . This technique offers an excellent opportunity tocross calibrate the energy scales of various subsystems, e.g. , to calibrate the photon energy scale against the mo-mentum scale of the tracking systems in e + e − → µ + µ − γ events. While in principle also the beam energy spec-trum can be obtained from this method, it suffers fromlarge event-by-event statistical fluctuations due to therelatively large width of the Z resonance [234].But also in the case that there is no photon detected,the amount of collinear beamstrahlung or ISR energy canbe reconstructed from kinematic constraints on an event-by-event basis. In this case, however, the measured mo-menta of the fermions have to be used. The previously1mentioned case of e + e − → µ + µ − γ , then provides an ex-cellent method for an in-situ determination of the beamenergy spectrum, since the muon momentum scale canbe calibrated to 10 ppm from J/ψ → µ + µ − decays [234].In presence of beam polarisation, another impor-tant observable becomes accessible, namely the left-rightasymmetry of 2-fermion processes: A LR = σ LR − σ RL σ LR + σ RL (22)The parameters σ LR , etc. , are the chiral cross sections forfully polarised beams, defined in Sec. 4.10. Their relationto the cross section for partial polarisation is described inthat section. Here, we will focus on the measurement ofthe polarised cross sections and of angular distributionsfor the various 2-fermion processes. e + e − → f f analyses Di-fermion production at a center-of-mass energy of250 GeV has recently been studied both by ILD andSiD, albeit with complementary goals. ILD has per-formed a study of all di-lepton channels in full detec-tor simulation, including all leptonic 2-fermion and 4-fermion backgrounds and focussing on events with √ s (cid:48) >
230 GeV [236, 237]. After a simple cut-based event selec-tion, purities of 97-99% can be obtained, while retain-ing a signal of 26 million events in the e + e − case andof about 0.75 million events in the µ + µ − case and 0.6million events in the τ + τ − case. The polar angle distri-butions of the selected events are then compared to thepredictions of various BSM models, which fall into twoclasses: tree-level exchange of additional, E Z (cid:48) bosons and loop-effects from dark matter candidateson the γ/Z propagator. In the case of the Z (cid:48) models,the reach for a 3 σ observation ranges between 1.6 and4.8 TeV, depending on the exact model, while it is be-tween 165 and 460 GeV in case of the dark matter mod-els, again depending on the exact type of model. Thesenumbers so far combine only the electron and muon chan-nels, therefore further improvement is expected once the τ -channel has been included in the combination.SiD on the other hand has performed a study focussingon the measurement of A LR from radiative returns to the Z pole. They studied inclusively all di-lepton and di-jetchannels in fast detector simulation [238]. Thereby theymake use of the method mentioned above in order to ob-tain the boost between the Z rest frame and the lab framefrom the angles of the two leptons or jets. After a sim-ple cut-based event selection, about 4.5 million hadronic Z events and about 0.5 million leptonic Z events remainover a background of 1.2 million events for 250 fb − with P ( e − , e + )=(-80%,+30%). Exploiting the modified Blon-del scheme [239, 240] in order to extract A LR directlyfrom the polarised cross sections measured in the fourdifferent beam helicity configuraions, the estimated un-certainty on A LR for the full 2 ab − is ∆ A LR = 0 . A LR is extracted from a global fit to severalphysics processes, which is, in contrast to the modifiedBondel scheme, fully robust against unequal absolute po-larisation values when flipping the sign of the polarisa-tion. For more details on the discussion of the impactof polarisation on the control of systematic uncertaintiessee Sec. 8.3. e + e − → τ + τ − In the special case of e + e − → τ + τ − , the decays of the τ lepton can be used to determine their polarisation,which adds extra information about the Zτ τ vertex. Forthe polarisation measurement, the individual τ decaymodes have to be identified and treated separately. Ithas been shown in full simulation of the ILD detector at √ s = 500 GeV [5, 241] that the leptonic decay modes canbe identified with efficiencies and purities of about 99%.For the π and ρ decay modes as well as for the three-prong τ → a ν τ decay, the same study reached puritiesof 90% at efficiencies between 96% and 91%, while forthe one-prong τ → a ν τ decay efficiencies and purities ofabout 70% were achieved. In a more recent study [242],covering only the separation of the hadronic decay modes,efficiencies and purities of about 90% were demonstratedalso for the three-prong decay.After a polarisation analysis of the leptonic channelsand the π and ρ channels via an optimal observable tech-nique, the polarisation of the τ leptons can be measuredwith a relative uncertainty of about 1% already with anintegrated luminosity of 500 fb − . e + e − → bb The couplings of the b -quark are of particular interest be-cause as a lighter sister of the top-quark, it could be par-tially composite in extensions of the SM. Also, a ratherlarge discrepancy in the sin θ eff values extracted fromthe measurement of the foward-backward asymmetry of bb production at LEP and the A LR measurement at SLDstill persists today and could be easily confirmed or re-jected by remeasuring bb production at the ILC 250. Theprospects for this measurement have recently been eval-uated in full, GEANT4-based simulation of the ILD de-tector [235, 243].Thereby the special difficulty is to distinguish the b -quark from the b -quark. This can either be achieved byreconstructing the charge sum of the tracks from the b / b decay vertices, which requires highest efficiency and pre-cision for the reconstruction of tracks, also at small mo-menta and in the forward region — or via the charge ofKaons identified via their specific energy loss in the TimeProjection Chamber of ILD, see Sec. 6.3.1.2 b q cos - - - - - GeneratedReconstructedCorrectedZ return background backgroundccZZ ZH WW background b q cos - - - - - - - - - b q cos - - - - - GeneratedReconstructedCorrectedZ return background backgroundccZZ ZH WW background
FIG. 68: Polar angle distribution cos θ b of generated b -quarks and final reconstructed b -jets including any SM backgroundremaining after event selection. Left: P ( e + , e − ) = (+100% , − θ b . Right: P ( e + , e − ) = ( − , +100%). From [235]. Figure 68 compares the cos θ distribution of the b -quark at the generator-level, at reconstruction-level andafter all corrections applied, for both opposite-sign po-larisation configurations. Both techniques for identifyingthe b -direction, vertex charge and Kaon ID, have beencombined here and contribute about equally to the finalevent sample. These distributions are then used to ex-tract the left- and right-handed couplings of the b -quarkto the Z -boson and the photon — or alternatively formfactors F γ/Z A/V . The expected precisions on a subset ofcouplings and form factors is compared to the corre-sponding LEP results in Fig. 69. The ILC projectionsin this plot are based on only 500 fb − at 250 GeV,corresponding to the data collected in the first couple ofyears before the luminosity upgrade. For the full data set,further improvement by about a factor of 2 is expected.
10. PHYSICS SIMULATIONS: TOPQUARK
In this section, we will review the highlights of the topquark program of linear colliders. Since the top quarkhas not yet been studied in e + e − reactions, its studyat a linear collider gives the opportunity to dramaticallyimprove the precision with which we know its properties.As we have explained above, such precision measurementcan reveal clues to the origin of the large mass of the topquark and possibly, through this, to the nature of theHiggs interactions that give mass to all fermions. Thepotential of linear e + e − colliders for top quark physics isdiscussed in more detail in the ILC design reports [5, 138]and in Refs. [244–246]. g F Z1V F Z1A F ZL g ZR g R e l a t i v e p r e c i s i on [ % ] -
10 110
ILC 250 GeVLEP 91 GeV
ILD
FIG. 69:
Comparison of the LEP measurements to theexpected precision at the ILC. The results of the ILCcorrespond to the integrated luminosity of L I = 500 fb − tobe collected at √ s = 250 GeV before the luminosity upgrade.Final results for the full 250 GeV dataset would improve theprecision further by about a factor of 2. From [235].
The e + e − → tt production process has a sizeablecross section above the top quark pair production thresh-old. With a left-handed electron beam and right-handedpositron beam the cross section reaches approximately 1pb at √ s = 500 GeV . Top quark pair production, withthe top quarks decaying to a W -boson and a bottom3quark, is the leading six-fermion process. Most recentsimulation studies [246–248] have focused on the the lep-ton+jets final state, where one of the W -bosons decays toa charged lepton and a neutrino and the other W -bosonto jets. Compared to the fully hadronic final state [249],the lepton + jets final state offers the advantage of thepresence of an energetic charged lepton, that helps to tagtop and anti-top quarks and is an efficient polarimeter.The selection of top quark pair events at the ILC isstraightforward. For lepton+jets events the requirementof a charged lepton and two b-tagged jets is sufficient toreduce the Standard Model background. The efficiencyof the selection can be very high, between 50 and 80%depending on the purity requirement.The complete reconstruction of the tt system is morechallenging. The assignment of the six fermions to topand anti-top quark candidates suffers from combinatoricsthat can lead to significant migrations in differentialmeasurements. Their effect on observables such as theforward-backward asymmetry are kept under control bya rigorous selection on the reconstruction quality. Thesize of potential systematic effects due to the selectionand reconstruction of the complex six-fermion final stateis then expected to be sub-dominant [247]. Later studieshave extended this conclusion to a broader set of observ-ables [246, 248, 250].To take full advantage of the large integrated lumi-nosity envisaged in the ILC operating scenario, a rigor-ous control of experimental and theoretical uncertaintiesis required. Ultimately, we expect that the data-driventechniques developed for the bottom-quark analysis ofRef. [235, 243] will supply an in-situ measurement of therate of wrong combinations. This will allow one to cor-rect differential measurements using the statistical powerof the entire data set.A complete and quantitative analysis of systematiclimitations is currently ongoing. The results presentedin this section are based on the prospects of Ref. [246–248]. Where needed, results are extrapolated to the fullintegrated luminosity of 4 ab − . The top quark mass is a fundamental parameter of theStandard Model that must be determined experimentally.Precise measurements are essential for precise tests of theinternal consistency of the Standard Model, through theelectro-weak fit [251] or the extrapolation of the Higgs po-tential to very high energy scales [252]. The precise valueof the top quark is also needed as input to the theoryof flavor-changing weak decays [253] and models of thegrand unification of the fundamental interactions [254].The top quark pair production threshold was identifiedlong ago [255] as an ideal laboratory to measure the topquark mass, and other properties such as the top quarkwidth and the Yukawa coupling and the strong couplingconstant [256]. The large natural width of the top quarkacts as an infrared cut-off, rendering the threshold crosssection insensitive to the non-perturbative confining part of the QCD potential and allowing a well-defined crosssection calculation within perturbative QCD. This cal-culation has now been carried out the N LO order [257]with NNLL resummation [258]. Fully differential resultsare available in WHIZARD [259].Given this precise theoretical understanding of theshape of the tt threshold cross section as a function ofcenter of mass energy, it is possible to extract the valueof the top quark mass by scanning the values of thiscross section near threshold. We emphasize that the topquark mass determined in this way is, directly, a short-distance quantity that is not subject to significant non-perturbative corrections. It is also closely related to the MS top quark mass, the input to the theory calculationslisted above. The uncertainty in the conversion is lessthan 10 MeV [260]. This contrasts with the situation athadron colliders, where the conversion uncertainties, thenonperturbative corrections, and the experimental sys-tematics in the measured top quark mass contribute in-dependent uncertainties, each of which is about 200 MeV.A simulation of the threshold scan is presented inFig. 70. The scan of the tt threshold measures the topquark pair production cross section at ten e + e − center-of-mass energy points. The error bars on the pseudo-datapoint represent the statistical uncertainty of the measure-ment, the uncertainty band indicates the theory (scale)uncertainty of the calculation. A fit of the line shape willgive a precise extraction of the top quark mass [261–263].The statistical uncertainty on the threshold mass is re-duced to below 20 MeV with a scan of ten times 20 fb − .The total uncertainty on the MS mass can be controlledto the level of 50 MeV . These systematic uncertain-ties include a rigorous evaluation of theory uncertaintiesin the threshold calculation and in the conversion to the MS scheme [264].The top quark mass can also be measured precisely inoperation above the tt threshold. The top quark masscan be extracted from the differential cross section of ttγ events as a function of the center of mass energy of the tt system √ s (cid:48) = √ s (1 − E γ / √ s ), as shown in Fig. 70. A fitwith a calculation that matches the NNLL prediction forthe threshold region with an O ( α s ) calculation for thecontinuum yields a statistical uncertainty with 100 MeVfor 4 ab − at 500 GeV [246]. Including the theoryuncertainty due to scale variations and experimental sys-tematic uncertainties the total uncertainty is estimatedto be below 200 MeV .A direct mass measurement can reach a statistical pre-cision below 100 MeV [263] and will be helpful to clarifythe interpretation of such measurements.A linear e + e − collider can thus achieve a precision thatgoes well beyond even the most optimistic scenarios forthe evolution of the top quark mass measurement at theLHC.4
340 345 350 [GeV]s c r o ss s e c t i on [ pb ] threshold - QQbar_Threshold NNNLOttISR + ILC Luminosity Spectrum 1.37 GeV t G PSt default - m 0.1 GeV – variations t m 0.15 GeV – variations t G theory uncertainty efficiencies and signal yields from EPJ C73, 2530 (2013) February 2019 simulated data points total -1
200 fb
340 360 380 400 [GeV]s' e v en t s / b i n = 500 GeVs at -1 Pseudo-data 4 ab ) = 165 GeV t (m t ), m a NNLL + O( 500 MeV) – ) t (m t ), m a NNLL + O(Systematic uncertainty (scale)
FIG. 70: Two methods to extract the top quark mass:(upper panel) a scan of the center of mass energy throughthe top quark pair production threshold, and (lower panel) areconstruction of the differential ttγ cross section as afunction of s (cid:48) during operation at √ s = 500 GeV . Among the direct searches for physics beyond theStandard Model with top quarks in the final state, thesearches for flavour changing neutral current interac-tions of the top quark have been studied in most de-tail. Thanks to the excellent charm tagging performanceand the clean experimental environment such searches atthe ILC can compete with the sensitivity of the LHC toanomalous tZc , tHc and tγc couplings.Searches for e + e − → tc production can already beperformed during the 250 GeV stage [265]. Greatersensitivity can be achieved in searches for t → Hc and t → γc decays above the tt production threshold. Basedon full-simulation studies [246, 266] scaled to an inte-grated luminosity of 4 ab − at a center of mass energyof 500 GeV , the 95% C.L. limits on FCNC branchingratios are expected to reach BR ( t → Hc ) ∼ × − and BR ( t → γc ) ∼ − , well in excess of the limits expected after 3 ab − at the HL-LHC. Composite Higgs models and models with extra dimen-sions naturally predict large corrections to the top quarkcouplings to the Z and W bosons [267–269]. The studyof top quark pair production at an e + e collider thereforeprovide a stringent test of such extensions of the SM.The potential of the 500 GeV ILC for the measurementof the cross section and forward-backward asymmetry in tt is characterized in detail in Ref. [247]. It is importantto note that these measurements search for deviationsfrom the SM in the main production mechanism of the tt system through s -channel γ and Z exchange. Withtwo configurations of the beam polarization, measure-ment of the angular distribution, and measurement vari-ables sensitive to the t and t polarizations, all 6 possible CP -conserving form factors can be disentangled and con-strained at the 1% level. Especially designed CP -odd ob-servables can also provide precise and specific constraintson the CP -violating form factors [248]. The expected68% C.L. limits on the form factors with 500 fb − at acenter of mass energy of 500 GeV are compared to theHL-LHC expectation of Ref. [270, 271] in Fig. 71.The corrections to the top quark electroweak couplingscan be parametrized by set of dimension-6 operators ofthe SM EFT that contain the top quark as a field. Thereis a large number of such operators, although the re-striction to e + e − reactions allows us to concentrate ona limited set of operators that appear at the tree levelin electroweak pair production. Because the top quarkis massive, helicity conserving operators such as chiral4-fermion operators and helicity violating operators thatgive corrections to the top quark magnetic moments mustbe considered on an equal footing.In Ref. [250], the authors consider the perturbation ofthe reaction e + e − → tt by the 10 dimension-6 operatorsthat contribute to the cross section at the tree level. Theyshow that a combination of the 500 GeV run, with ex-cellent sensitivity to two-fermion operators, with 1 TeVdata, with increased sensitivity to four-fermion opera-tors, yields tight constraints independently on all opera-tor coefficients. This study demonstrates the feasibilityof a global EFT analysis of the top sector at the ILC. Italso gives an expected sensitivity of the ILC to top elec-troweak couplings that exceeds that of the HL-LHC pro-gramme by one to two orders of magnitude. Translatedinto discovery potential for concrete BSM scenarios, alinear collider operated above the top quark pair produc-tion threshold can probe for compositeness of the Higgssector to very high scales, up to 10 TeV and beyond [269].Figure 72 presents the results of a combined fit of theWilson coefficients dimension-six operators that affectthe electroweak interactions of bottom and top quarks.For each operator, limits are extracted from existing LEPI and LHC run 2 data and from prospects for the high-luminosity stage of the LHC and for ILC runs at √ s =5 g F Z1V F Z1A F g F Z2V F U n c e r t a i n t y - - - Phys.Rev.D73 (2006) 034016Phys.Rev.D71 (2005) 054013 -1 = 14 TeV, L = 3000 fbsLHC, EPJ C75 (2015) 512 -1 = 500 GeV, L = 500 fbsILC, PRELIMINARY -1 = 380 GeV, L = 500 fbsCLIC, PRELIMINARY ~ 3%) th.uncert. s ( -1 = 380 GeV, L = 500 fbsCLIC, ] g Re[F ]
Z2A
Re[F ] g Im[F ]
Z2A
Im[F - - -
10 1 U n c e r t a i n t y Phys.Rev.D73 (2006) 034016 , Phys.Rev.D71 (2005) 054013 -1 = 14 TeV, L = 3000 fbsHL-LHC, -1 = 500 GeV, L = 500 fbsILC initial, -1 = 500 GeV, L = 4000 fbsILC nominal, -1 = 380 GeV, L = 500 fbsCLIC initial, -1 = 3 TeV, L = 3000 fbsCLIC, FIG. 71: The ILC prospects for the measurement of theelectroweak couplings of the top quark, expressed as 68%C.L. bounds on the form factors in a general expression forthe Lagrangian that describes the ttZ and ttγ vertices:(upper panel) CP-conserving form factors from Ref. [272],and (right) CP-violating form factors, from Ref. [248].
250 GeV and 500 GeV .The LHC measurements in the top quark sector are ex-trapolated to the complete program, including the high-luminosity phase of the LHC. The detailed analyses pre-sented in Ref. [273] predict that significant progress canbe made, especially in the measurements on rare asso-ciated processes. The HL-LHC scenarios S1 and S2 are defined in analogy to the two scenarios defined for Higgscoupling measurements in Ref. [126]. Both contemplate3 ab − at √ s = 14 TeV , but assume a very differentscaling of the systematic uncertainties. In scenario S1systematic uncertainties are fixed to today’s values; in S2the experimental systematic uncertainties scale with in-tegrated luminosity like the statistical uncertainties andtheory uncertainties are reduced by a factor of 2 withrespect to the current state of the art.The ILC250 scenario includes measurements of thecross section and forward-backward asymmetry of bot-tom quark pair production, with a total integrated lu-minosity of 2 ab − divided between the left-right andright-left beam polarizations, following Ref. [235]. TheILC500 prospects includes in addition the projections at √ s = 500 GeV of Ref. [250] for top-quark pair pro-duction, scaled to an integrated luminosity of 4 ab − at √ s = 500 GeV .The Z -pole data yield tight constraints on coefficientsof operators that are specific to the bottom quark C ϕb and C dW . The current LHC constraints on the top quarkoperators, from single top production, top quark decayand associated ttX production are relatively weak. Theoperator coefficients C / ϕ , that affect both bottom-quarkand top-quark interactions have tight individual limitsfrom LEP, but are poorly constrained in a global fit. TheS2 scenario for the HL-LHC foresees a significant increaseof the precision of the measurements. The 250 GeV runat the ILC considerably sharpens the limits on the op-erators that affect the bottom-quark interactions with Z -bosons and photons. Finally, with the 500 GeV data,the operators specific to the top quark, the dipole opera-tors C tB and C tW and the operator that C ϕt that mod-ifies the right-handed coupling of the top quark. Withrespect to the current precision the constraints on all op-erator coefficients are expected to improve by one to twoorders of magnitude. The increase in precision is very sig-nificant even with respect to the most aggressive scenariofor the HL-LHC.Similar analyses, now requiring only 4 relevantdimension-6 operator coefficients, can improve the con-straints on four-fermion operators involving b , c , andlight-fermion sectors beyond the results projected inSec. 9.2. As with the trilinear Higgs coupling, the top quarkYukawa coupling can be measured either directly or indi-rectly. In the literature, most estimates of the accuracyof determination of the top quark Yukawa coupling aredone within the simple context of the SM with only thisone parameter varied. We will first quote uncertaintieswithin this model in this section and then explore theimplications of a general EFT analysis.Consider first the indirect determination of the topquark Yukawa coupling. For the Higgs boson decays H → gg , H → γγ , and H → Zγ , there are no SM6 t j C j C j C RtW C RtB C b j C RbW C - - -
10 110 ] - [ T e V i C D LEP1 + LHC Run 2 + HL-LHC S1 + HL-LHC S2 + ILC250 + ILC500
FIG. 72: The 68% C.L. limits on the Wilson coefficients of the dimension-six operators that affect the electroweakinteractions of the top and bottom quark. The filled bars indicate individual limits, from a single-parameter fit, while thedashed bars present the marginalized limits of a seven-parameter fit. The first bar indicates the current limits, obtained in afit to LEP I and LHC run 2 measurements. These results are compared with prospects for the HL-LHC, with 3 ab − at √ s = 14 TeV . The S1 and S2 scenarios are defined in analogy with the Higgs scenarios of Ref. [126]: S1 envisages noimprovement of the systematic uncertainties, while S2 foresees that theory uncertainties can be reduced by a factor 2 andexperimental systematic uncertainties are expected to scale with 1 √ s . The green bars indicate the 250 GeV and 500 GeVruns of the ILC, with 2 ab − . tree diagrams and so diagrams with top quark loops giveleading contributions. For h → gg , the top quark loop di-agram gives the single largest contribution. In Tab. XX,it is shown that the ILC program up to 500 GeV willdetermine the effective coupling in this process to bett-ter than 1%. Even higher precision can be obtained in ajoint fit including also the top quark radiative correctionsto the cross sections for e + e − → ZH , e + e − → ννH , and e + e − → γH [274]. However, one should be uncomfort-able that, for this determination, the simple model is toosimple, since new heavy colored particles can also con-tribute to these processes at the 1-loop level.An indirect determination that calls out the top quarkmore specifically is the measurement of the influence ofthe top quark Yukawa coupling on the shape of the tt pair production cross section very close to the tt thresh-old, due to the Higgs boson-exchange contribution to the tt potential. In principle, this effect could give a 4% de-termination of the Yukawa coupling if the QCD theoryof the top quark threshold region were precisely known.However, the Higgs-exchange effect is of the same size asthe N LO QCD corrections. At this time, the thresholdshape is calculated only to this N LO order, by the useof a very sophisticated NRQCD framework [257], com-bined with NNLL resummation of large logarithms [258].Propagating the QCD uncertainties gives an uncertaintyof 20% on the top quark Yukawa coupling [245], and thereis no clear path at this time to improve the accuracy of the QCD result.A more direct – and more robust – extraction of the topquark Yukawa coupling is possible from measurements ofthe cross section of the associated production process ofa Higgs boson with a top quark pair. In the SM the pp → tth and e + e − → tth production rates are simplyproportional to the square of the Yukawa coupling. Thefirst measurements of the tth rate at the LHC [275, 276]have an uncertainty of approximately 30% and are ex-pected to improve considerably during the remainder ofthe LHC program [126].At an electron-positron collider, the cross section for tth production increases rapidly above √ s ∼
500 GeV,reaching several fb for √ s = 550 GeV. Detailed studiesof selection and reconstruction of these complex multi-jetevents have been performed by the ILC at 500 GeV [277]and 1 TeV [5, 278] and by CLIC at 1.5 TeV [246]. Thedirect measurement of the top quark Yukawa coupling atthe ILC reaches 2.8% precision [129], with 4 ab − at550 GeV. With a sample of 2.5 ab − at 1 TeV, thisprecision would improve to 2% [108]. From the energy-dependence of the cross section and the top polarizations,this reaction can also be used to probe for non-standardforms of the tth coupling [279].In principle, the corrections to the top quark elec-troweak couplings and to the top quark Yukawa couplingshould be parametrized by dimension-6 operators of theSM EFT. The studies of Refs. [280, 281] show that the in-7direct extraction of the Yukawa coupling from the hgg or hγγ vertices do not provide robust measurements of thetop quark Yukawa coupling in a general multi-parameterfit. The indirect determination is certainly very sensitiveto new physics in the Higgs sector, but in case a deviationfrom the Standard Model predictions is observed, furthermeasurements are needed to unambiguously identify theoperator that gave rise to the effect.The direct determination from the tth rate, be it atthe LHC or at the ILC, is more robust. However, evenin this case vertices arising from dimension-6 operatorsthat do not directly involve the Higgs boson can affectthe cross section for e + e − → tth and thus create am-biguity in the extraction of the top quark Yukawa cou-pling. In e + e − → tth , the EFT corrections arise from4-fermion eett operators and from operators that correctthe γ and Z anomalous moments of the t quark. Sim-ilarly, in hadron-hadron collisions, the cross section for gg → ttH is corrected by dimension-6 operator that al-ter the top quark vector coupling to gluons and thosewhich create a possible axial vector coupling to gluonsand a gluonic magnetic moment. The 34-parameter fiton current LHC data of Ref. [282] indeed finds that themarginalized limits on the operator C tϕ that shifts thetop quark Yukawa coupling are considerably weaker thanthe individual constraints and the results of fits withfewer parameters.The LHC and a linear e + e − collider offer excellentopportunities to probe the interaction between the topquark and the Higgs boson, both directly and indirectly.In a global EFT fit the coefficients of all operators affect-ing the Higgs branching ratios and tth production ratemust be constrained to sufficient precision, such that thecoefficient of the operator that shifts the Yukawa couplingcan be extracted unambiguously. Precise measurementsat a linear collider operating above the tt threshold pro-vides powerful constraints to such a fit.
11. GLOBAL FIT TO HIGGS BOSONCOUPLINGS, AND COMPARISONS OFILC TO OTHER COLLIDERS
In this section, we make use of the simulation resultspresented in Secs. 8 and 9 to present projections for theuncertainties in Higgs boson couplings that will be ob-tained from the ILC. We will present projections bothfor the 250 GeV stage and for the stage that includes at500 GeV in the centre of mass, following the plan pre-sented in Sec. 3.
To extract Higgs boson couplings from measurements,we will use the method of Effective Field Theory (EFT)sketched in Sec. 4.6. This method has been explained infull technical detail in [3, 218]. Here we will present an
FIG. 73: Feynman diagrams contributing to the process e + e − → Zh when contributing dimension-6 operators areincluded. overview of the EFT analysis, supplying those technicaldetails that are relevant to the evaluation of our fittingprocedure.In the EFT method, we represent the effects of newphysics on the Higgs boson and other SM observablesby the most general linear combination of dimension-6operators invariant under SU (2) × U (1). In the mostgeneral settting, this formalism contains a very largenumber of parameters. However, in the special case of e + e − collisions, there are some simplifications. First, forthe purpose of computing deviations from the SM dueto dimension-6 operators, it suffices to work at the elec-troweak tree level. (The basic SM predictions must ofcourse be computed as accurately as possible, typically to2-loop order in electroweak couplings.) Second, it sufficesto consider only CP-even observables, since the contribu-tions of CP -odd operators can be bounded by indepen-dent measurements. With these simplifications, a total of16 operator coefficients appear in the analysis. One addi-tional parameter c appears in double Higgs production,and 10 additional parameters appear in analyses of topquark production, but these do not enter the extractionof the Higgs couplings we will discuss here.To determine these operator coefficients, we can useprecision electroweak measurements and data on e + e − → W + W − in addition to data from Higgs processs. Theanalysis also makes use of specific constraints from theLHC that should be available when the ILC runs andhave a clear model-independent interpretation. Theseare the ratios of branching ratios of the Higgs boson tothe final states γγ , ZZ ∗ , Zγ , µ + µ − . The measurementsof these four channels are all based on Higgs bosons pro-duced centrally through the dominant gluon fusion pro-cess. The ratios of rates should be extracted from LHCdata in a way that most systematic errors are commonand cancel in the ratios. It is shown in [3, 218] thatthis data suffices to determine these coefficients indepen-dently and without important degeneracies. The way that we make use of LHC inputs illustrates thecomplementarity of LHC and ILC results on the Higgs An 17th operator contributes to G F but is controlled by con-straints from the measurement of e + e − → µ + µ − at high energy.The bound from LEP 2 is already very strong. P r e c i s i on o f H i gg s bo s on c oup li ng s [ % ] Z W b t g c inv G h G g g Z · m · Impact of improved TGC precisions ILC250 ¯ HL-LHC ILC250, TGCs from LEP ¯ HL-LHC
Model Independent EFT Fit LCC Physics WG
FIG. 74: Projected Higgs boson coupling uncertainties whenincluding the charged triple gauge coupling precisions asexpected from ILC250, compared to the case of using thecorresponding LEP results instead.coupling 2 ab − at 250 + 4 ab − at 500 HZZ
HW W
Hbb
Hτ τ
Hgg
Hcc
Hγγ
HγZ
Hµµ
Htt - 6.3
HHH - 27Γ tot inv other
Htt and
HHH couplings; thusno model-independent values are given in these lines. Thebottom lines give, for reference, the projected uncertaintiesin the Higgs boson total width, the 95% confidence limits onthe Higgs boson invisible width, and the 95% confidencelimits on possible exotic Higgs decay processes that are notexplicitly recognized, as described in the text. The analysis,which based on SM Effective Field Theory, is highlymodel-independent boson. The LHC has special strength in gathering statis-tics on rare modes of Higgs decay, especially those withleptons in the final state. On the other hand, resultsfrom the ILC are needed to determined the Higgs totalwidth and the absolute normalization of branching ratiosand partial widths with minimal model assumptions. Ina similar way, the HL-LHC will probe deeply for spe-cific exotic decays of the Higgs boson, especially thoseinvolving muons, while ILC is needed to survey the mostgeneral possibilities for exotic decays.Here is an outline of the analysis. We need to fit 16 op-erator coefficients plus 4 SM parameters which are shiftedby dimension-6 effects. The 16 EFT coefficients arise inthe following way: 2 from Higgs boson operators ( c H , c T ), 4 from operators involving the squares or cubes ofSM gauge field strengths ( c W W , c W B , c BB , and c W ), 3from Higgs current couplings to leptons ( c HL , c (cid:48) HL , c HE ),5 from the operators that shift the Higgs coupling to b , c , g , τ , µ , and two more from Higgs current couplings toquarks ( c W and c Z ).The parameters are constrained rather specifically, ina way that we can outline. Measurements of α and G F and the W , Z and H masses constrain the SM parametersplus one additional parameter ( c T ). Purely leptonic pre-cision electroweak measurements (Γ( Z → (cid:96) + (cid:96) − ) and A (cid:96) )constrain two of the three c H(cid:96) parameters, and measure-ments of the W and Z total widths fix c W and c Z . Mea-surements on e + e − → W + W − constrain the third c H(cid:96) parameter, plus c W B and c W . The LHC measurementof the ratio of branching ratios Γ( h → γγ ) / Γ( h → ZZ ∗ )will put a strong constraint on c BB . The Higgs branch-ing ratios to fermion and gluon states constrain those5 parameters. At this point, only the parameters c H and c W W remain. These are constrained, respectively,by the normalized cross section for e + e − → ZH and thepolarization asymmetry or angular distribution in thisreaction.To account for the possibility of non-standard Higgsboson decays, we add two more parameters to our globalfit. The first is the Higgs branching ratio to invisible de-cay products. This is independently measurable at an e + e − collider using the Z tag in e + e − → ZH . The sec-ond is the branching ratio to exotic modes that somehowdo not correspond to any category that has been pre-viously defined. Though it might be argued that anyHiggs decay mode above the 10 − level of branching ra-tio should be directly observed, we add this parameter asinsurance against modes not yet thought of. It is deter-mined by the constraint that the Higgs branching ratios,including this one, sum to 1. We call this possible con-tribution to the Higgs width Γ other .The ratio of the Higgs couplings to W and Z plays animportant role in the extraction of Higgs boson couplingsand the Higgs boson total width. In the κ formalism,one parameter is assigned for each of these couplings,and these parameters are determined independently fromHiggs production cross sections. This typically leads tovery small errors on the Z coupling and large errors on9 P r e c i s i on o f H i gg s bo s on c oup li ng s [ % ] Z W b t g c inv G h G g g Z · m · t · l · ILC250 ¯ HL-LHC ILC500 ¯ ILC250 ¯ HL-LHC dark/light: S1*/S2*
Model Independent EFT Fit LCC Physics WG
FIG. 75: Projected Higgs boson coupling uncertainties for the ILC program at 250 GeV and an energy upgrade to 500 GeV,using the highly model-independent analysis presented in [4]. This analysis makes use of data on e + e − → W + W − in additionto Higgs boson observables and also incorporates projected LHC results, as described in the text. The darker bandscorrespond to the values given in Tab. XVI. The lighter bands correspond to the scenario S2* in Table XX, which is definedin the discussion of Sec. 11.3. The column λ refers to the HHH coupling. In the last four columns, all bars are rescaled bythe indicated factor. the W coupling. In the EFT formalism, as we have shownin Eq. 8, two parameters are needed to describe each ofthese couplings, making the κ description oversimplified.The corresponding W and Z parameters are linked bynot-so-simple formulae involving other EFT parameters.However, these formula can be evaluated with the helpof data from precision electroweak and W W reactions,leading to constraints that are at the same time tight andhighly model-independent [218]. This is one illustrationof the synergies between different measurements that theEFT method brings into play.It is remarkable that, though the EFT analysis intro-duces a large number of free parameters, each one has adirect counterpart in a physical observable that can bemeasured in the e + e − environment. In particular, beampolarisation is very powerful in providing needed infor-mation. For example, in the EFT framework, the process e + e − → ZH involves three diagrams, shown in Fig. 73.Only the first diagram appears in the SM. The third di-agram is required to be small by precision electroweakconstraints. The second diagram, with s -channel γ ex-change, is generated by the operator corresponding tothe coefficient c W W . Under a spin reversal e − L ↔ e − R ,the Z diagram flips sign while the γ diagram keeps thesame sign. Thus, measurement of the polarisation asym-metry in the total cross section for e + e − → ZH directlymeasures the c W W parameter. Beam polarisation plays another important role. With beam polarisation, thebranching ratios of the Higgs boson are measured for twodifferent polarisation settings. The statement that thesame branching ratio must appear in each pair of mea-surements helps to sharpen the global fit. At the sametime, this comparison provides a check of assigned sys-tematic errors. In Sec. 11.2, we will assess the importanceof polarisation quantitatively and present results on thetrade-off between polarisation and increased luminosity.The precise measurement of the triple gauge bosonscouplings expected at the ILC also plays an importantrole in global fit. We have described the measurement ofthese couplings through analysis of e + e − → W + W − inSec. 9.1. The ILC is expected to improve the precisionof our knowledge of these couplings by a factor of 10over results from LEP and by a similar large factor overresults from LHC. Figure 74 shows the significance of thisset of inputs. In the figure, the results of our global fit,in green, are compared to the same fit using as inputsthe LEP constraints on the triple gauge boson couplings.From this analysis, we derive the projected uncertain-ties on Higgs couplings shown in Tab. XVI. Here andin the rest of this section, the uncertainty presented inthe tables for each HAA coupling is defined to be halfof the fractional uncertainty in the corresponding partialwidth. In cases such as
HZZ in which multiple EFT co-efficients contribute to a given partial width (see Eq. 8),0the quoted uncertainty includes the uncertainties in theseEFT parameters and their correlation.Table XVI is the main result of this report in relationto the ILC capabilities for Higgs boson coupling measure-ments. This table gives the current state of our under-standing of the ILC capabilities. We emphasise that theanalysis leading to these projections is completely model-independent, in the sense that all models of new physicsdescribable either by the addition of local operators tothe SM EFT (for heavy new particles) or by the addi-tion of invisible and exotic Higgs decays (for light newparticles) are included. Given the run plan and detectordesigns described above, we have a high degree of confi-dence that these estimated uncertainties will be achieved– and, probably, surpassed – in the realisation of the ILCprogram. The projections in the table are summarised inFig. 75. e + e − Higgs factory pro-posals
In this section, we will present a comparison of thecapabilities of the ILC for precision Higgs measurementwith those of other proposed linear and circular colliders,including CLIC, CEPC, and FCC-ee. We will presentthree sets of quantitative comparisons.To begin, each collider proposal has presented its ownset of projections in its documentation for the Euro-pean strategy study. We have copied the relevant num-bers for projected Higgs boson coupling uncertainties intoTab. XVII. For colliders other than the ILC, those esti-mates have been made using the more model-dependent κ fit. The small values of the ZZ coupling uncertainty rela-tive to the W W coupling uncertainty reflects the model-dependence of the κ formalism as discussed in Sec. 11.1.It is interesting to ask how the proposals would com-pare if a common fitting technique is used. In almost allcases, the measurement errors are dominated by statis-tics and the efficiencies used in the analyses are similar.A direct way to make the comparison is to use the resultsof our ILC analyses to estimate efficiencies and statisti-cal errors for all of the colliders. That is, we assumethe luminosity samples in the collider proposals, assumethe same measurement errors per unit of luminosity usedto generate Tab. XVI, take account of differences in thecross sections resulting from the use (or not) of polarizedbeams, and rerun our fitting program for those condi-tions. This is the method used to generate Tab. 3 ofRef. [3]. As a proxy for CEPC, we assume a sample of5 ab − at 250 GeV without polarisation. As a proxyfor FCC-ee, we use a sample of 5 ab − at 250 GeVplus 1.5 ab − at 350 GeV, without polarisation. Therun plan for CLIC includes only 1 ab − at 380 GeVbefore the energy upgrade to 1 TeV. Since we are un-comfortable using the EFT formalism with dimension-6operators only at 1 TeV and above, we represent CLICby a sample of 2 ab − , similar to ILC, with 80% e − po-larisation only, at 350 GeV. The results are presented inTab. XVIII and visualised in Fig. 76. Though not all differences among the various proposalsare included in this table, the table does usefully showhow increased luminosity trades off against beam polar-isation. We see that beam polarisation is a very power-ful tool, essentially compensating the advantage of largerevent samples claimed by the circular machines. Notethat the advantage is not uniform; increased luminosityis a generally greater benefit for smaller couplings suchas Hcc , while polarisation has special benefit for spe-cific couplings such as
HγZ . The comparison of 2 ab − data samples at 250 and 350 GeV is also interesting, sincethe two energy settings bring different advantages to theHiggs physics study.To make the comparison in Tab. XVIII more realis-tic, we should indicate how the improved precision elec-troweak measurements that can be achieved at circu-lar colliders affect these numbers. The answer to thisquestion is given in Tab. XIX, which is compared withTab. XVIII in Fig. 77. For the ILC columns, we haveassumed that the input measurement of A (cid:96) , the polari-sation asymmetry of the lepton- Z coupling, will be im-proved by a factor 10 by measurement of the polarisa-tion asymmetry in e + e − → Zγ at 250 GeV. This is oneof the improvements to our Higgs analysis currently un-der study listed in Sec. 8.4. The improvement in A (cid:96) by a dedicated “Giga-Z” run at the Z pole would becomparable [138]. For the third and fourth columns,we assume the improvements in measurements of pre-cision electroweak observables described in the FCC-eeCDR [284].The ILC results with polarised beams are somewhatimproved in the most precisely determined couplings bythe improvement in the input A (cid:96) . The changes for circu-lar colliders, which make use of the large improvementsfrom Z pole running, are more significant for the resultsat 250 GeV. More surprisingly, though, the improvementin precision electroweak inputs turns out to make only asmall difference when the dataset at 350 GeV is added.One reason for this, pointed out in Ref. [218], is thatthe EFT coefficients responsible for precision electroweakcorrections also contribute terms of order s/m Z to the e + e − → ZH cross section. Then these coefficients arepowerfully constrained by comparing measurements ofthis cross section at different centre-of-mass energies. Finally, we compare the capabilities of the ILC for pre-cision Higgs measurement to those of the HL-LHC.In Sec. 4, we have presented qualitative comparisonsof the approach to Higgs physics that is possible at theILC to the approach that must be taken at the LHC.Here we will compare the quantitative projections givenin Sec. 11.1 to the projections presented in the HL-LHCYellow Report [126]. The comparison is not so straight-forward because of the different frameworks used in theanalyses. In Tab. XX, we quote projected uncertaintiesin Higgs boson couplings for HL-LHC given in Ref. [126]1 P r e c i s i on o f H i gg s bo s on c oup li ng s [ % ] Z W b t g c inv G h G g g Z · m · t · l · Impact of Luminosity, Energy and Polarisation 250 GeV polarised -1 - e + e ¯ HL-LHC 500 GeV polarised -1 - e + e ¯ ... 250 GeV unpolarised -1 - e + e ¯ HL-LHC 350 GeV unpolarised -1 - e + e ¯ ... Model Independent Fit LCC Physics WG
FIG. 76: Projected Higgs boson coupling uncertainties for selected scenarios from Table XVIII. In particular it shows that at √ s = 250 GeV, 2 ab − with polarised beams yield comparable results to a much larger data set of 5 ab − with unpolarisedbeams. P r e c i s i on o f H i gg s bo s on c oup li ng s [ % ] Z W b t g c h G g g Z ·
250 GeV unpolarised -1 - e + e ¯ HL-LHC 350 GeV unpolarised -1 - e + e ¯ ... 250 GeV polarised -1 - e + e ¯ HL-LHC 500 GeV polarised -1 - e + e ¯ ... dark/light: current / improved EWPO Model Independent EFT Fit LCC Physics WG
FIG. 77: Impact of improved electroweak precision observables on the projected precisions for various Higgs couplings for thecombinations of luminosity, energy and polarisation from Tab. XIX. For the unpolarised cases, EWPO projections from theFCC-ee CDR [284] have been assumed, while for the polarised case only an improved precision for A (cid:96) is assumed. Couplingsfor which there is no improvement due to improved EWPO have been omitted from the figure. The notation of the figure isthe same as that in Fig. 75. ILC250 ILC500 CEPC FCC-ee CLIC350 CLIC1.4 CLIC3coupling EFT fit EFT fit κ fit κ fit κ fit κ fit κ fit HZZ
HW W
Hbb
Hτ τ
Hgg
Hcc
Hγγ
Hµµ
Htt - 6.3 - - - 3.0 3.0
HHH - 27 - - - 35 9Γ tot inv < inv is similar to that for CEPC. For CLIC, the values are taken from Ref. [285], Tab. 2,with HHH values from Ref. [215]. All values are given in percent (%). The bottom lines give, for reference, the projecteduncertainties in the Higgs boson total width and the 95% confidence limits on the Higgs boson invisible width. For ILC,CEPC, and FCC-ee, the values given for the γγ and µµ modes are those combined with expected LHC results.2/ab-250 +4/ab-500 5/ab-250 + 1.5/ab-350 2/ab-350coupling pol. pol. unpol. unpol e − pol. HZZ
HW W
Hbb
Hτ τ
Hgg
Hcc
Hγγ
HγZ
Hµµ
Htt - 6.3 - - -
HHH - 27 - - -Γ tot inv other ± and present results from the ILC global fit in a numberof scenarios.The projections in Ref. [126] are based on operationalexperience with detectors that have successfully mademeasurements on the Higgs boson, have exceeded theirexpectations from the proposal stage, and, based onthat experience, expect further improvements beyond thelevel of their current methodologies. These estimates arebased on extrapolation of current results. They do de-pend on the assumption that the improvement of theATLAS and CMS detectors by the Phase-II upgradeswill fully compensate for the effects of the high-pileupenvironment expected at the HL-LHC. With this under- standing, these estimates give the expectations for theperformance of the ATLAS and CMS experiments in theHL-LHC program.In addition to the formal HL-LHC projections, whichare ATLAS/CMS combinations, the individual LHC ex-periments have actually produced two sets of projections,a final one (S2) described above and a maximally conser-vative one (S1) that includes the increase in statisticsfrom HL-LHC but uses only current methodologies andcurrent estimates of systematic errors. It is interestingto us to compare the S1 and S2 projections, since thiscomparison gives an idea of the improvements expectedby the LHC experiments beyond the current state of the3 HZZ
HW W
Hbb
Hτ τ
Hgg
Hcc
Hγγ
HγZ
Hµµ
Htt - 6.3 - -
HHH - 27 - -Γ tot inv other A (cid:96) , as discussed in Sec. 8.4. In thesecond two columns, the unpolarised collider projections from from Tab. XVIII are modified to include the improvement ofthe uncertainties on precision electroweak observables described in the FCC-ee CDR [284]. art to the end of the HL-LHC program. In Tab. XX wehave quoted both the S1 numbers from CMS (those fromATLAS are similar) and the final (S2) projections fromRef. [126]. At the S2 level, the systematic errors are esti-mated to be small enough that the projections benefit byabout 20% from making an ATLAS/CMS combination.We call to the reader’s attention the fact that the im-provements projected for HL-LHC from the current AT-LAS and CMS uncertainties on the HZZ and
HW W couplings are very significant already in the S1 analysis.This is because the high statistics of the HL-LHC allowsone to make use of the vector boson fusion productionmode, which has a low cross section but relatively smalltheoretical and modelling uncertainties. On the otherhand, the projected improvement in the
Hbb couplingsis based mainly on a higher-precision understanding ofanalyses such as that shown in the upper plot of Fig. 45.The ILC estimates have a very different basis. It isalways risky to estimate errors for experiments that havenot yet been constructed or taken data. We have de-signed the ILC detectors to have the superb performancecharacteristics detailed in Secs. 6 and 7. As far as ispossible today, these projected performances are justi-fied by R&D and test beam measurements. However,from this point, we wished to be quite conservative. Wethen take the expected precision of our measurements tobe those of our current analyses of fully simulated, digi-tised events. This conservative choice is the basis of theestimates quoted in Sec. 11.1. Experience at all othercolliders has shown that final precision with real dataexceeds such a priori estimates.To compare these projections with those for HL-LHC,we have defined four scenarios, called S1*, S1, S2*, S2.The projections in Tab. XX labeled S1* are those fromTab. XVI in Sec. 11.1. While, as we have stressed, the ILC analysis is highly model-independent, the LHC anal-ysis relies on certain model assumptions that are difficultto remove with only the constraints available at a hadroncollider. The LHC results in Tab. XX assume that theHiggs boson has no decay modes beyond those predictedin the SM, and they assume that the Higgs boson cou-plings to
W W and ZZ are modified only by a rescaling.In the ILC EFT analysis, each of these these couplings de-pends on two additional independent constants ζ W and ζ Z defined in Eq. 8. For a sharper comparison, then,we have then recast the ILC EFT analysis adding thesetwo assumptions, that is, assuming no Beyond-Standard-Model decays and assuming ζ W = ζ Z = 0. This givesthe set of values labelled S1. We do foresee some im-provements in our analyses, as described in Sec. 8.4.These reflect improvements to our methods that are un-der study and seem promising but are not yet completelyvalidated. Making these improvements gives the uncer-tainties S2* and S2 (for model-independent and model-dependent EFT fits) quoted in Tab. XX. These estimatesare intended give an indication that the ILC capabilitesare not fixed but rather are improvable with further ex-perimental effort. We remind the reader that all esti-mates quoted for ILC require certain specific inputs fromHL-LHC, as explained in Sec. 11.1. Our use of HL-LHCresults nicely illustrates the complementarity of the twomachines, as is discussed in that section.It is subtle to directly compare the projections for HL-LHC and ILC taking into account their two differentphilosophies. On the ILC side, since we have no experi-ence with the actual operation of the detectors and theaccelerator, we have been very cautious in making ex-trapolations beyond our current full-simulation results tothe actual performance that we might eventually achieve.We therefore regard our scenario S1, and even our sce-4 P r e c i s i on o f H i gg s bo s on c oup li ng s [ % ] Z W b t g c g m · t · l · HL-LHC arXiv:1902.00134S1: CMS, S2: ATLAS&CMS ILC250 ¯ HL-LHC ILC500 ¯ ILC250 ¯ HL-LHC dark/light: S1/S2 =0 & no anom. hZZ/hWW coupl.)
BSM G Fit ( k Model Dependent EFT / LCC Physics WG
FIG. 78: Projected Higgs boson coupling uncertainties for the LHC and ILC using the model-dependent assumptionsappropriate to the LHC Higgs coupling fit. The dark and light red bars represent the projections in the scenarios S1 and S2presented in Ref. [126]. The dark and light green bars represent the projections in the ILC scenarios S1 and S2 described inthe text. The dark and light blue bars show the projections for scenarios S1 and S2 when data from the 500 GeV run of theILC is included. The notation of the figure is the same as that in Fig. 75. nario S2, to be more conservative than the final (S2) HL-LHC projections. In any event, we hope that we havedescribed the various estimates given in Tab. XX clearlyenough that the reader can make his or her own judge-ment as to the most appropriate comparison of the ILCto the HL-LHC.In all cases, however, it is only the ILC results thatcross a boundary into the region in which we can robustlyclaim discovery of deviations from the SM of the sizegenerally expected in new physics models.In summary, Figs. 75 and 78 illustrate the capabili-ties of the ILC and the comparison of the ILC and LHCprojections. Figure 75 shows the uncertainty projectionsfor the 250 GeV stage of the ILC, in the highly model-independent framework S1*. These results are comparedto results obtained in the same framework with the ad-dition of data from an energy upgrade to 500 GeV. Thisjustifies the statement made earlier that deviations fromthe SM seen at the 250 GeV stage of the ILC can be con-firmed with an independent data set after the upgradeto higher energy. Figure 78 shows the comparison of theILC projections in the S1 and S2 scenarios to the projec-tions given for the S1 and final (S2) HL-LHC projectionsgiven in Ref. [126]. Note that, while the improvementfrom the S1 to S2 scenarios for ILC is a matter of conjec-ture, the improvement from the 250 GeV to the 500 GeVvalues is based on completed full-simulation studies.
12. PHYSICS SIMULATIONS: DI-RECT SEARCHES FOR NEW PARTI-CLES
In this section, we will discuss the prospects at theILC for the direct discovery of new particles. Our dis-cussion will of course be given in the context in whichthe LHC experiments have carried out a large numberof new particle searches, some reaching deeply into themass region above 1 TeV. Still, we will explain, experi-ments at e + e − colliders can bring a new approach to newparticle searches and still have very interesting windowsfor discovery.In general, the new particle searches done at the LHChave focused on scenarios within each theory of newphysics that give the best possible experimental prospectsto observe new physics. However, a negative result willonly make it possible to claim that new physics is ab-sent in a specific region of the full theoretical parameterspace. There is no guarantee that new physics would bediscovered even if it is within the kinematic reach of theexperiment. The actual parameters of the theory mightbe far from the ones giving the searched-for signature.It is a rather different perspective to concentrate on the worst possible points in the theoretical parameter space.This clearly cannot reach as far out as in the previouscase, but now a negative result would make it possible5 coupling current S1* S1 S2* S2 HZZ - LHC 11. 2.4 1.5- ILC 250 0.57 0.46 0.47 0.37- ILC 500 0.38 0.20 0.33 0.18
HW W - LHC 15. 2.6 1.7- ILC 250 0.55 0.44 0.47 0.36- ILC 500 0.37 0.19 0.33 0.18
Hbb - LHC 29. 6.0 3.7- ILC 250 1.0 0.83 0.80 0.69- ILC 500 0.60 0.43 0.49 0.37
Hτ τ - LHC 17. 2.8 2.0- ILC 250 1.2 0.98 0.97 0.86- ILC 500 0.77 0.63 0.68 0.59
Hgg - LHC 15. 4.0 2.5- ILC 250 1.6 1.6 1.2 1.2- ILC 500 0.96 0.91 0.75 0.70
Hcc - LHC - - -- ILC 250 1.8 1.8 1.4 1.3- ILC 500 1.2 1.1 0.90 0.85
Hγγ - LHC 15. 2.9 1.8- ILC 250 1.1 1.1 1.1 1.0- ILC 500 1.0 0.97 1.0 0.96
HγZ - LHC 15. 9.8- ILC 250 9.1 9.1- ILC 500 6.6 6.3
Hµµ - LHC 70. 6.7 4.3- ILC 250 4.0 4.0 4.0 4.0- ILC 500 3.8 3.7 3.8 3.7
Htt - LHC 14. 5.5 3.4- ILC 500 6.3 4.1 4.5 2.8
HHH - LHC 80 50- ILC 500 27 27 20 20Γ tot - LHC 28 5 4- ILC 250 2.4 1.4 1.9 1.1- ILC 500 1.6 0.70 1.3 0.60Γ inv - LHC 26 3.8- ILC 250 0.36 - 0.36 -- ILC 500 0.32 - 0.32 -Γ other - LHC- ILC 250 1.6 - 1.4 -- ILC 500 1.2 - 1.1 -TABLE XX: Projected uncertainties in the Higgs bosoncouplings for HL-LHC and for ILC with the specific LHCinputs described in the text, in various scenarios. All valuesare given in percent (%). The precise definition of a Higgscoupling uncertainty for the ILC EFT analysis is given atthe end of Sec. 11.1. The values labelled “current” are takenmainly from Table 8 of the CMS publication Ref. [286]; thevalues for Γ tot and Γ inv are found in the text of Sec. 8.2 andSec 3.9, respectively. The LHC S1 values are those from the κ fit to CMS projections, given in Tab. 36 of Ref. [126]; theATLAS projections are similar. The S2 values are thosefrom the ATLAS/CMS combination given in Fig. 30 ofRef. [126]. Values for the HHH coupling are found in thetext of Sec. 3.2 of Ref. [126]. Values for Γ tot and Γ inv arefound in the text of Sec. 2.7.1 and Sec 6.1, respectively, inRef. [126]; these are CMS results only. For ILC, the S1*results are those presented in Sec. 11.1 for ILC programs at250 GeV and 500 GeV. The scenario S1 includes the samevalues for ILC measurement uncertainties but also includesadditional model-dependent assumptions that are used inthe LHC S1 analysis. These are described in the text. Thescenarios S2* and S2 assume the improved performance inILC measurements presented in Sec. 8.4. to claim that the new physics theory is ruled out at all possible parameter values below the kinematic reach ofthe experiment. It would also make discovery of the newphysics guaranteed if it is indeed energetically reachable.These two avenues in the search for new physics arein fact the main difference between searches at hadroncolliders and lepton colliders. Hadron colliders are wellsuited for the first approach, with their large reach intounknown territory in energy, but are less well suited forthe second one due to huge background levels and tothe initial state being unknown. Lepton colliders have alower reach in energy, but excel in fully exploiting all pos-sible manifestations of new physics within reach. Whencomparing exiting limits on new physics from LHC orLEP, commonly presented in the mass-plane of a pair ofnew states, one must note that the former are incompleteones showing models than might be excluded (for some- but not all - other model parameters), while the lattershows complete ones, i.e. models that must be excluded( for any value of other parameters).ILC—like LEP—will explore all corners of the param-eter spaces of theoretical models. It offers a guaranteeddiscovery within the kinematic reach of the machine and,in the case of no discovery, sets immutable limits that canbe the final word the models it considers. In this section,we will concentrate on this aspect, explaining how ILCwill expand the region of fully-explored theory space be-yond that of LEP.It is clear that an ILC operating at 500 GeV, or evenat 1 TeV, will vastly extend the fully explored region.But, already at 250 GeV, ILC will significantly extendthis region: While it is true that 250 GeV is not muchmore than the maximum energy of 208 GeV that LEPreached, there are other features that are amelioratedby orders of magnitude: The luminosity is 1000 timeshigher, and both beams are polarised. The beam-spot issub-microscopic in size, allowing to find displaced verticesat much smaller distances, also in channels (like (cid:101) τ pairproduction), where there is no reconstructable primaryvertex. Furthermore, many aspects of the detectors arebetter than the LEP ones by a factor ten or more. Sincecomputing power has been increased by orders of magni-tude, all interactions can be recorded and analysed, i.e.no trigger will be needed for experiments at the ILC, un-like the conditions at LEP. Taken together, this meansthat much more subtle effects can be probed for at ener-gies that in principle were reachable at LEP.Many of these features also are relevant in exploitingLHC’s blind-spots: namely any signal stemming fromprocesses without QCD interactions, or with only softfinal states. Here, trigger-less operation of almost fullyhermetic detectors is a great advantage. Processes whereonly kinematic reconstruction of the full event would re-veal BSM physics, can be studied at a lepton collider. Incontrast, at a pp collider, only partial reconstruction inthe transverse plane is possible. In addition, ILC detec-tors will be more precise than their LHC counter-parts,since the low background-rates means that it is not neces-6sary to compromise between performance and radiation-hardness.We will discuss a few particular classes of signatures,which have been studied in depth: • Pair-production of new short-lived states decayingto visible SM particles and another lighter newstate, the lighter state being invisible, the so-called antler signatures. R-parity conserving SUSY is anexample. • Production of new invisible final states, where onlythe presence of initial state radiation could revealnew phenomena, the mono-photon signature. Aprominent example is dark matter production. • Production of new scalars, similar to the SM Higgsboson, but with smaller coupling to the Z , and pos-sibly very different decay branching ratios, the new-scalar signature. Here nMSSM and 2HDM modelsare typical examples.In addition to these cases discussed in detail, otherextensions to the SM can be searched for at the ILC.Compared to a hadron collider, a lepton collider is muchless dependent on missing energy signature to find newphysics. For example, in R-parity violating SUSY ormodels with visible signs of a dark sector, or in com-posite models, new physics does not necessarily manifestitself with a missing energy signature, but rather by thepresence of new states. New physics could also manifestitself as new couplings, rather than new particles, e.g. ,in unexpected flavour signatures. ILC-250 would be ableto probe such signatures, in some cases with a sensitiv-ity equal to that of dedicated flavour experiments, likeBELLE II or LHCB. In general, due to the low back-ground levels, the ILC can be used to search for any newparticle in nature with electromagnetic, hyper-charge orelectroweak quantum numbers and thus provides discov-ery potential complementary to that of the LHC. A com-prehensive overview of the potential of the full ILC pro-gram to discover new particles and phenomena can befound in [136]. A event-signature that often occurs in BSM theories isthe “antler” topology. In such processes, a pair of (notnecessarily identical) new states are produced. Theseparticles then decay into SM particles and a lighter newstate. The lighter state might further decay to other SMparticles, and an even lighter new state. At the end ofsuch a cascade of decays, a detector-stable new state, χ ,is produced, which is not directly detectable. The prop-erties of the visible decay-products not only reveals thepresence of physics beyond the standard model, but alsocontain a large amount of information about the proper-ties of the new states.In the case of direct decays of a pair of new state(s)(denoted by X and Y ) produced in an e + e − collision at E lab = E cms = M o , the endpoints of the energiesof the standard model particles x and y in the processe + e − → XY → xyχχ can be found to be E i max ( min ) = M (cid:32)(cid:115) λ ,X,Y + 4 M M i (cid:48) M (cid:112) λ i (cid:48) ,i,χ + 4 M i (cid:48) M i M i (cid:48) +( − ) (cid:115) λ ,X,Y M (cid:112) λ i (cid:48) ,i,χ M i (cid:48) (cid:33) (23)where the shorthand λ k,l,m = λ ( M k , M l , M m ) is used ,and i (cid:48) is either X or Y (and similarly, i is the correspond-ing SM particle, either x or y )[287]. By determining theseendpoints of the energy-spectra of the two SM particles( x and y ), and using the knowledge of E cms , M x and M y ,both M χ , M X and M Y can be determined. If the twoinitially produced new particles have the same mass, sothat M X = M Y = M i (cid:48) , then λ ,X,Y = M − M o M i (cid:48) .If, in addition, the masses of the produced SM particlescan be neglected, λ i (cid:48) ,i,χ = ( M i (cid:48) − M χ ) . Hence, in theimportant case of pair production, e + e − → Y Y → yyχχ with M y ≈
0, one finds the simpler relation E y max ( min ) = E cms (cid:32) − (cid:18) M χ M Y (cid:19) (cid:33) +( − ) (cid:115) − (cid:18) M Y E cms (cid:19) (24)from which M χ and M Y can be determined from theend-points.R-parity conserving SUSY is a model that predicts avariety of antler-type signatures, in sfermion or bosinoproduction. The lightest SUSY particle (the LSP) wouldbe the final, undetectable, new state, and would usuallybe the lightest neutralino, (cid:101) χ , even though other candi-dates also would be possible. Both pair-production andassociated production can occur, and the decays mightbe direct or in cascades. The produced pair might befermions (bosinos), or scalars (sfermions), and can carrya variety of different quantum-numbers. Hence, an exten-sive study of SUSY covers a wide range of possible antlertopologies. The essential difference between SUSY andthe general case, is that SUSY predicts the couplings, bythe fundamental principle of SUSY: spaticles couples asparticles . From the experimental point of view, the im-plication of this is rather in the interpretation in terms ofexclusion- or discovery-reach, than in the actual analysis-methods required. In the SUSY case, regions in the mass-plane can be fully exploited, since the production cross-section is predicted. In the general case, the conclusionwould be that discovery or exclusion is possible down The K¨all´en function λ is defined as λ ( a, b, c ) = a + b + c − ab − ac − bc In [288], it is shown how experiments an e + e − collidercan systematically and exhaustively search for any Next-to-lightest SUSY Particle (NLSP), and thereby guaranteediscovery, or set immutable limits for SUSY within thekinematic reach of the accelerator.LHC has set no limits on processes giving the weakestlimits, such as sleptons in general, and staus in particular.In Refs. [289–291], it is shown that limits on selectronsand smuons can be set in the best possible case - eitherrequiring that not only that both selectrons and smuonshave the same mass, but also that the left- and right-handed states are degenerate, or that the mass differenceto the LSP is very large. No limits at all could be setfor stau production. One the other hand, LHC does givestringent limits on a gluino or first- or second-generationsquarks [292]. Also for a stop, the LHC coverage is in-creasing, and excludes a stop with a mass of 1 TeV, if theLSP mass is below 250 GeV [292, 293]. However, boththeoretically, and given these limits, it is quite unlikelythat a coloured sparticle would be the NLSP.Instead, the most stringent absolute limits on theNLSP comes from LEP. There limits on all SUSY parti-cles has been set. In [177, 294–296], searches for sleptonsare reported, in [177, 295, 297, 298], the results of thesearches for squarks can be found, and in [177, 299–301],the results for charginos and neutralinos are given. Inaddition, combined results can be found in [302].A summary of the LEP results is that a charginoNLSP below between 92 and 103 GeV (depending onthe mass-difference) is excluded, whatever the natureof the chargino is. For the second neutralino, a gen-eral exclusion in the mass-plane is not possible, due tothe complicated structure of the neutralino mass-matrix,which allows for situations where the cross-sections bothfor e + e − → (cid:101) χ (cid:101) χ and e + e − → (cid:101) χ (cid:101) χ can be smallat the same time. For any given SUSY model, how-ever, the combination of the searches for e + e − → (cid:101) χ (cid:101) χ ,e + e − → (cid:101) χ (cid:101) χ and e + e − → (cid:101) χ ± (cid:101) χ ∓ , as well as the searchesfor e + e − → (cid:101) e (cid:101) e and e + e − → (cid:101) ν e (cid:101) ν e (since the (cid:101) e and the (cid:101) ν e contribute to t-channel production of (cid:101) χ and (cid:101) χ ± , re-spectively) will be likely to yield constraints on M (cid:101) χ .In the slepton sector, smuons and selectrons are ex-cluded below 95 to 100 GeV, if the mass difference tothe LSP is above 4 GeV. Staus are excluded below 87to 93 GeV, if the difference is above 8 GeV. Selectronsand smuons are completely excluded below M Z / Z ), while staus are excluded below 28GeV for any mass-difference and mixing. The weakerlimit for the staus is due to the fact that it is possiblethat the stau mixing is such that it does not couple at all to the Z , only to the photon, and hence that the con-straint from the width of the Z cannot be applied. Infact, the limit from the stau at minimal cross-section isthe weakest limit on any NLSP candidate, and thereforerepresents the current absolute exclusion for any MSSMmodel.In addition, LEP excludes third generation squarks be-low 94 to 98 GeV at mass differences to the (cid:101) χ larger than8 GeV and the mixing angle giving the minimal cross-section are excluded. For any mixing, mass-differenceand dominant decay mode, a stop with mass below 63GeV is excluded. However, these coloured sector limitsare essentially superseded by the LHC ones.It can be noted that, except for the chargino, the LEPlimits fall short of the kinematic limit by 10 to 20 % evenfor large mass-differences, and for small differences by 50% or more. This is due to the fact that the size of thedata-sets at the highest energies were tiny - 500 pb − at 206 GeV, and only 33 pb − at 208 GeV. This lowluminosity is particularly unfavorable for the sfermions,because of the slow ( β ) rise of the cross-section close tothreshold. Also, the LEP detectors all were triggered,meaning that in the low mass-difference cases, eithersome auxiliary activity was needed to provide a trig-ger, or only a small fraction of the events - those wherethe detectable SM decay-products happened to be al-most aligned with the direction of the decaying sparticle -would be registered. This resulted in a quite low selectionefficiency in these cases. Furthermore, due to the largesize of the beam-spot at LEP, using impact-parametersas a tool to separate signal and background was not veryeffective. Finally, the beams at LEP were unpolarised,which is a particular draw-back when searching for signsof a chiral theory such as SUSY.In contrast, the ILC has none of these problems, asalready mentioned, which means that the ILC will largelyextend the territory explored by LEP. The same featuresof the ILC allows to probe for signals in the LHC blindareas for un-coloured states at lower mass differences.In [288], the prospects at the ILC at 500 are evaluated.Two cases were studied in more detail, the least and themost challenging ones, namely the cases where the NLSPis either the (cid:101) µ R or the (cid:101) τ . The first case profits from avery clean and well measured signal, with no other pa-rameters than the two masses involved, while the secondone has the most difficult signal (due to the partly in-visible SM system), and in addition has a further theoryparameter, namely the (cid:101) τ mixing angle. For both thesecases, the full mass-plane was scanned over a 1-by-1 GeVgrid, using the detailed fast simulation SGV, describedin 7.7. In the (cid:101) τ case, the mixing-angle was chosen suchthat the production cross-section was as small as possi-ble. The resulting exclusion/discovery reaches are shownin Fig. 79. One can note that the exclusion limit, evenfor the rather modest luminosity used in the study isonly 0.8 (4) % from the kinematic limit for the (cid:101) µ R ( (cid:101) τ ).Hence, the area of assured discovery-potential or powerof model-independent exclusion will increase by a factor8 E xc l udab l e a t % C L NLSP : µ ˜ R M NLSP [ GeV ] M L SP [ G e V ] (a) µ ˜ R M NLSP [ GeV ] M L SP [ G e V ] (b) E xc l udab l e a t % C L NLSP : τ ˜ M NLSP [ GeV ] M L SP [ G e V ] (c) τ ˜ M NLSP [ GeV ] M L SP [ G e V ] (d) FIG. 79: ILC discovery reach for a (cid:101) µ R (top) (cid:101) τ (bottom) NLSP for (cid:82) L dt = 500 fb − at √ s = 500 GeV. For the (cid:101) τ , themixing angle was chosen to give the lowest possible production cross-section. (a,c) full scale, (b,d) zoom to last few GeVbefore the kinematic limit [288]. of 6 to 7 with respect to current (LEP) results.Even for an ILC operating at 250 GeV, a substantialincrease in reach is expected. The area of the excludedmass plane will increase much more than the modest in-crease in energy might suggest at first glance. Reasonablyassuming that also at 250 GeV, reach will fall only a fewpercent short of the kinematic limit, the area covered byILC-250 will increase by 70 % to 80 % at large mass-differences compared to the LEP results. At the smallestmass-differences, even larger improvements might be ex-pected, once dedicated analyses have been performed inthis region. Also at 250 GeV, the reach into LHC’s blindareas will be important. In [287] and [303] more in-depth analyses of specific mod-els are presented. The emphasis in these works is to esti- mate the precision with which various parameters can beextracted. The analyses were done with the full SM back-ground simulated with full detector simulation at E cms =500 GeV. In [303], also the signal was simulated with fullsimulation, while the detailed fast simulation SGV wasused in [287] . In Fig. 80, the energy-spectra of the visi-ble decay-products of (cid:101) e R , (cid:101) µ and (cid:101) τ are shown. A numberof novel techniques were utilised to extract the relevantedges from the distributions (the truncated sub-samplemethod [287], and finite impulse response method [304]),both giving precisions a factor two or more better thantraditional methods. Once the edges were determined,applying Eq. 23, the masses of (cid:101) e R and (cid:101) µ R could be esti-mated with an error of 2 (cid:104) and 4 (cid:104) , respectively. Fitting The models studied allows for (cid:101) e R , (cid:101) µ R . and (cid:101) τ production also at E cms = 250 GeV lepton [ GeV ] l ep t on s / . G e V e ~R SMSUSYbkgSGV 500 GeV,500 fb -1 , P +80,-30 (a) lepton [ GeV ] l ep t on s / . G e V µ ~R SMSUSYbkgSGV 500 GeV,500 fb -1 , P +80,-30 (b) jet [ GeV ] j e t s / . G e V τ ~1 SMSUSYbkgSGV 500 GeV,500 fb -1 , P +80,-30 (c) FIG. 80: Property determination of SUSY (a) selectron. (b) muon and (c) τ -jet energies in selected di-leptons events aftercollecting 500 fb − of data for beam-polarisation P − , +30 [287]. for a single value of M (cid:101) χ in these two spectra, an errorof 1.5 (cid:104) was obtained. Using the value of M (cid:101) χ , andfitting spectrum in Fig. 80c for M (cid:101) τ , the (cid:101) τ mass couldbe determined to 2 (cid:104) .Furthermore, as can also be seen from Eq. 23, closeto the threshold, the decay-products become mono-energetic which means that an almost background-freethreshold-scan can be done at a collider – such as ILC –where E cms can be freely chosen. The result of such ascan is shown in Fig. 81. The precision of the masses arecomparable to those obtained from the fit to the spectra,but are independent of M (cid:101) χ . In addition, the fit to theshape of the threshold makes it possible to exclude thehypothesis that the new states discovered are fermions,as can be see by the fits of either σ ∝ β (expected forscalars) or σ ∝ β (expected for fermions).A further measurement possible in these models is thedetermination of the polarisation of the τ -lepton fromthe (cid:101) τ decay. This is achieved by studying the spectrumof the π :s in the τ → πν τ mode, or the ratio of E ± π to E π + E ± π in the τ → ρν τ → π ± π ν τ mode. In [303] itwas found that the degree of polarisation could be de-termined to ∼ (cid:101) τ pair-production could be deter-mined to 4 %. The difference in the cross-section whenthe beam-polarisations are reversed can be used to de-termine the (cid:101) τ mixing angle , which together with thedetermination of τ -polarisation can be used to determinethe size of the chirality-conserving gauagino fraction ofthe (cid:101) χ relative to it’s chirality-flipping higgsino fraction. The other possibility to determine the mixing-angle, namely the (cid:101) τ (cid:101) τ associated production have not yet been studied in detail In [287, 305–307] detailed studies of specific points wherea bosino is the NLSP are presented. Many differenttopologies are covered by the analyses, depending on themass-difference. The bosinos might decay to on-shell Z or W bosons, undergo three-body decays (mediated byvirtual Z or W bosons), or decay radiatively. In addi-tion, mixing in the bosino-sector will yield relations be-tween the masses of (cid:101) χ , (cid:101) χ ± and the LSP, relations thatare different for different models. The same is true forthe production cross-sections, in particular the relationbetween (cid:101) χ (cid:101) χ pair-production and (cid:101) χ (cid:101) χ associated pro-duction. Also assumed relations at the high scale haveimplications on the phenomenology at the EW-scale, inparticular on how large the LSP-NLSP mass differencecan be. For bosino production it is therefore needed tostudy various cases in detail, and avoid assumptions onother related processes. The LEP experiments all carriedout a comprehensive search for a (cid:101) χ ± NLSP which werecombined in [302]. For the (cid:101) χ NLSP case, as mentionedis section 12.1.1, only cross-section limits can be given, ifno assumptions on the model is done. Such limits weregiven by the experiments [177, 299, 301].At LHC, the reach of the search for the non-colouredbosinos can be quite large, but always with strong modelassumptions. Even so, the limits tend to disappear forlow mass-differences, and are largely absent in the regionallowed if GUT-scale unification of the bino and winomass-parameters ( M and M ) is assumed [289, 308, 309].Once again, the conditions at the ILC will allow to ex-tend the model-independent LEP limits to higher masses.Because the (cid:101) χ ± cross-section is quite large, and has asharp ( ∝ β ) threshold dependence, the increase in reachat ILC-250 with respect to LEP is not as large as itis for the sfermions: already LEP could exclude an (cid:101) χ ± NLSP to only a few GeV below the kinematic limit andat all mass-differences. However, the ILC potential be-0 √ s [ GeV ] σ ( e + e - → e ~ R e ~ R ) [ f b ] data 10 fb -1 / pointfit of β to data : δ M e ˜ = 190 MeVM e ˜ = 126.59 ± β to dataSGV P +80,-30 (a) √ s [ GeV ] σ ( e + e - → µ ~ R µ ~ R ) [ f b ] data 10 fb -1 / pointfit of β to data : δ M µ ˜ = 220 MeVM µ ˜ = 126.80 ± β to dataSGV P +80,-30 (b) FIG. 81: : Scans over the threshold for slepton production (a) scan of the e + e − → (cid:101) e R (cid:101) e R threshold (b) scan of thee + e − → (cid:101) µ R (cid:101) µ R [287]. comes very important at a 500 GeV, and even more soafter a future energy-upgrade to 1 TeV. Nevertheless, thelimit/discovery potential of ILC-250 is still sizeable com-pared to current and future LHC limits, in particularas the LHC limits for bosinos suffer more from model-dependence than the sfermion ones.This is illustrated by a specific example in figure 82,which shows the current limits in the M (cid:101) χ - M (cid:101) χ ± planefrom ATLAS [290], together with the projected discov-ery reach at 14 TeV with (cid:82) L dt = 3000 fb − [310] Hereit is assumed that M (cid:101) χ = M (cid:101) χ ± , that (cid:101) χ ± and (cid:101) χ arepure Winos, and that Br( (cid:101) χ → W ( ∗ ) /Z ( ∗ ) (cid:101) χ ) =1 .The brown-shaded area indicates the corresponding limitfrom LEP [177, 300, 311], which assumes only (cid:101) χ ± pairproduction, with no assumption on the decay mode, northe nature of the (cid:101) χ ± . The expected limits for the ILCat √ s = 500 or 1000 GeV are also shown with the sameassumptions as for the LEP exclusion. As can be seenfrom the (loophole) region not covered by the LHC, thereis a large discovery potential for the ILC, even after thehigh luminosity LHC data has been fully exploited. The case with antler topologies with small mass-differences is particularly interesting for ILC, already at250 GeV. Partly because the experimental limits fromLEP are much weaker then for high mass differences, andlargely absent at LHC, but also for theoretical reasons.One reason to particularly search for SUSY with smallmass-differences is the possibility that the LSP is the(full) explanation for Dark Matter: Over a large re-gion of SUSY parameter space, co-annihilation with the Note that the more difficult case (cid:101) χ → h ( ∗ ) (cid:101) χ is not considered. NLSP is an attractive mechanism which acts to reducethe relic density of the LSP to its cosmologically ob-served value [312]. An example of such a model is theone presented in [287] and discussed in the previous sec-tion. In this model, the NLSP is the (cid:101) τ , with a mass10 GeV above the LSP. Co-annihilation requires a smallmass difference between the NLSP and the LSP in orderto be effective, and thus the expected value of the relicdensity depends strongly on the exact masses and mix-ings of the involved particles, requiring measurements atthe permille and percent-level, respectively. This is dis-cussed in [313], where also a detailed analysis of the relic-density determination that the measurements presentedin [287] would imply. Figure 83a shows the precision ofthe fitted relic density relative to the model value. Inthe figure, the model value was chosen to be the centralvalue determined from cosmology using the observationsof planck [314]. It was also verified the other model-values were faithfully reproduced by the fit, see Fig. 83b.A second reason to search for such low mass-differenceprocesses, applying to SUSY is that they tend to occurin many possible SUSY scenarios, as shown in Fig. 84,because of the mass-relations between different bosinosin the Wino- and Higgsino-sectors, the second lightestbosino will be close in mass to the LSP, if the latter isdominantly Wino or Higgsino. Only in the case of a largeadmixture of Bino in the LSP can the mass-difference bearbitrarily large. Furthermore, if GUT-scale unificationof the Bino and Wino mass parameters M and M holds,the next-to-lightest bosino cannot be heavier than twicethe LSP mass [315].In fact, light higgsinos are a fundamental requirementof natural SUSY models. The generic formula relating1
100 150 200 250 300 350 400 450 500 [ G e V ] m < m m Z = m - m m = m m (cid:1)(cid:2) = m ±1 (cid:1)(cid:2) m Z W ATLAS
All limits at 95% CL
FIG. 82: Discovery or exclusion regions in the M NLSP − M LSP plane for a (cid:101) χ ± or (cid:101) χ NLSP. Solid brown area: LEP exclusion;Solid red and dashed grey/blue lines: ATLAS exclusion (observed and expected), for the 8 TeV data (thinner lines) and the13 TeV data (thicker lines). Dashed green line: ATLAS 14 TeV discovery projections for (cid:82) L dt = 3000 fb − ; Dashed magenta(orange) lines: ILC discovery expectation for E CMS = 500 (1000) GeV; Solid black line: below line, no GUT scale gauginomass unification. The symbols indicate the positions in the mass-plane of the analyses mentioned in the text. The magentasolid area is the ATLAS low ∆( M ) search at 13 TeV, which however is within a different model. STC10' Ω / fit Ω P D F STC10' SUSY+hSTC10' SUSYSTC10' SUSY+xs+h (a) model Ω / fit Ω P D F STC10' SUSY+h75 SUSY+h Ω STC10'- 50 SUSY+h Ω STC10'-STC10'-LH150 SUSY+h (b)
FIG. 83: (a) Comparison of relic density fitted to the measurements of the SUSY model to the model value, with or withoutusing input from ILC higgs-measurements and with, in addition, using measured cross-sections. (b) Comparison betweenfitted and model value, when the model value was by hand modified as indicated. From [313]. M Z to SUSY parameters reads [316]: m Z m H d + Σ dd ) − ( m H u + Σ uu ) tan β (tan β − − µ (cid:39) − m H u − µ (25)To avoid unnatural fine-tuning between the terms on theright-hand side in this expression, each term should in-dividually be of the order of the left-hand side, i.e. , M Z ,and in particular µ should be as close as possible to M Z .This leads to a dominantly higgsino LSP and that also (cid:101) χ and (cid:101) χ ± are mainly higgsino. Mass differences withinthe higgsino sector are small, typically below 20 GeV, de- pending on the values of the other SUSY parameters, inparticular on M and M . The other SUSY particles canbe more heavy: top squarks may range up to ∼ ∼ (cid:101) χ and (cid:101) χ ± can be easily detected — with-out any need to rely on large-mass-gap decays of heav-ier particles. The ILC capabilities have been studied indetector simulations performed for different benchmarkpoints with mass differences ranging from 770 MeV [305]to 20 GeV [306]. Two examples of the striking signals2
100 200 300 400 500 600 700 [GeV] – c~ m [ G e V ] c~ m ) ,M < M m Higgsino-like LSP ( : [0.05,2] TeV m , ,M M : [1,70] b tan (a)
100 200 300 400 500 600 700 [GeV] – c~ m [ G e V ] c~ m ) m , < M Wino-like LSP (M : [0.05,2] TeV m , ,M M : [1,70] b tan (b)
100 200 300 400 500 600 700 [GeV] – c~ m [ G e V ] c~ m ) m , < M Bino-like LSP (M : [0.05,2] TeV m , ,M M : [1,70] b tan (c) FIG. 84: M (cid:101) χ vs M (cid:101) χ ± when scanning over the bosino parameters M , M , tan β and µ . (a) Higgsino-like LSP ( µ < M , M ),(b) Wino-like LSP ( M < µ, M ), (c) Bino-like LSP ( M < µ, M ). and the extraction of kinematic endpoints are given inFig. 85. The resulting precisions on masses and polarisedcross sections reach the percent level even in the experi-mentally most difficult cases and allow to determine otherSUSY parameters. They will also play an important rolein unveiling the nature of dark matter: in this case withthe result that the LSP only contributes a small fractionof the total abundance. Such a situation might call foradditional, non-WIMP constituents of dark matter suchas axions. In [317], it is shown that an ILC operating at1 TeV would have guaranteed discovery/exclusion reachover the entire class of natural SUSY models, which isillustrated in Fig. 86 for the example of the NUMH2model [318]. Only highly fine-tuned, un-natural, modelswould still be allowed if ILC at 1 TeV failed to discoverSUSY. No such statement can be expected to come outof HL-LHC: even though discovery would be possible atHL-LHC, no guarantee is possible. The primary probe at the ILC for the direct produc-tion of WIMP dark matter are photons emitted as initial-state radiation in association with the pair production ofdark matter. Such a Mono-photon search is analogous toMono- X searches at the LHC. The main backgrounds tothis search are the radiative neutrino production, whichis irreducible, and the radiative Bhabha scattering pro-cess, in which the outgoing electron and positron escapeundetected in the beam pipe. At LEP, searches for pho-ton events with missing energy were performed [320],and were later re-analysed within the effective operatorframework [321] .The prospects to detect WIMPs with such methodsat the ILC and to determine their properties have been Note that under LEP or ILC conditions the effective field the-ory approximation is accurate, while it is questionable in similaranalyses at hadron colliders. studied for a centre-of-mass energy of 500 GeV in detaileddetector simulation [106, 322]. Also at the ILC, the ex-perimental sensitivity have been interpreted in the frame-work of effective operators. Figure 87a shows the exclu-sion reach found, and Fig. 87b shows the extrapolationof these results to a wide range of integrated luminositiesand centre-of-mass energies [106]. For the full 500 GeV-program of the ILC, scales of new physics (Λ) of up to3 TeV can be probed, while the 1 TeV-energy-upgrade ofthe ILC would extend this even to 4 . X searches, it is essential to complement the pictureby probing the WIMP-lepton couplings at an electron-positron collider. Moreover, while LHC can probe larger3 /GeVs’
200 250 300 350 400 450 500 E v en t s / G e V γ χ∼ χ∼ γ χ∼ χ∼ SM simul. data 1.0 GeV ± = 168.6 fit ± χ∼ M dM770 (a) (GeV) mm E E v en t s / ( G e V ) SignalSUSY bkgSM bkg (b)
FIG. 85: Higgsino mass determination for (a) the charged higgsino from the recoil against an ISR photon in a scenario witha mass splitting of 770 MeV [305], using the SGV detector simulation. (b) the neutral higgsino from the energy of its visibledecay products in a scenario with a mass splitting of 10 GeV [306], using full detector simulation.FIG. 86: The m / vs. µ plane in the NUHM2 model for tan β = 15, m = 5 TeV, A = − m A = 1 TeV. We showcontours of the naturalness measure ∆ EW [319] along with current limits from LHC13 and future reach of HL-LHC and ILC.Location of benchmark points is indicated in green. WIMP masses due to its higher centre-of-mass energy,ILC can probe smaller couplings, thus higher energyscales for the WIMP-electron interaction due to its higherprecision.
In many models with extended Higgs sectors, e.g. , TwoHiggs Doublet Models, The Next-to-Minimal Supersym-metric Standard Model and Randall Sundrum models,there exists a light scalar S , lighter than the Standard4 [GeV] c M
50 100 150 200 250 [ G e V ] L ILDH20 (500GeV) e xc l u s i on r eg i one x pe c t ed W I M P EFT not valid
Effective operatorsvectoraxial-vectorscalar (a) [GeV]s
200 400 600 800 1000 ] - i n t. l u m i no s i t y [f b [ T e V ] L V e c t o r : =(80%,-30%) + ,e _ P(e (b)
FIG. 87: Left: Observational reach (3 σ ) of the ILC for a Spin-1 WIMP in terms of WIMP mass and κ e for three differentchiralities of the WIMP-fermion couplings Right: Expected sensitivity for a vector operator in an EFT-based interpretationas a function of integrated luminosity and centre-of-mass energy [106]. Model Higgs. The coupling of the S to the Z can bevery small, compared to the coupling a standard modelHiggs with the same mass would have to the Z . Sucha light scalar with suppressed couplings to the Z bosonwould have escaped detection at LEP. With a factor of1000 higher luminosity and polarised beams, the ILCis expected to have substantial discovery potential forthis kind of states. Furthermore, searches for additionalscalars at LEP and LHC are usually dependent on themodel details, in particular on the decay branching ratiosof the new scalar. Thus, to be able to search for such newstates, it is paramount to have a more general analysiswithout model-dependent assumptions. The recoil-masstechnique, in particular with the Z boson decaying intoa pair of leptons, offers the possibility to achieve this.The OPAL collaboration at LEP searched for lightscalars with this method, but the results were limiteddue to the low luminosity [324]. The large luminosityoffered by the ILC makes the recoil mass technique cor-respondingly more powerful [108] Therefore a search fora light scalar with a very weak interaction with the Z bo-son using the model-independent analysis would becomeviable at the ILC-250.A study was performed using the full GEANT4-basedsimulation of the ILD concept. As a preliminary re-sult [325], exclusion cross-section limits for masses of thenew scalar between 10 and 120 GeV are given in termsof a scale factor k with respect to the cross-section of theStandard Model Higgsstrahlung process would have had,would the Higgs-mass have been the one assumed for thenew scalar.Background events are rejected by considering kine-matic variables only relied on muons and the recon-structed Z : The invariant mass, transverse momentumand polar angle of the muon pair, as well as the polarangle of the missing momentum, and the polar angle of each muon, and the angle between them. Thus, no in-formation on the decay of S is used, and the resultswill indeed be model-independent. The recoil mass dis-tributions obtained after applying the cuts are shown inFig. 88a, for a number of hypotheses on the mass of S ,and k = 1.The main backgrounds depend on the scalar mass.In the small mass region, the two fermions backgrounde + e − → µ + µ − with an energetic ISR photon is theoverwhelming background; while in the Z -pole region,e + e − → ZZ → µ + µ − + X is an irreducible background,as is - obviously - e + e − → Z ∗ → ZH → µ + µ − H at M S ∼ M H . The two fermion background can be furtherrejected by taking into account ISR photon return effects.The ISR photon veto cuts are applied to the ISR photonsin the centre region and forward region, separately.The obtained 2 σ expected exclusion limits for the crosssection scale factor k are shown for scalar mass from10 GeV to 120 GeV in Fig. 88b. It is one to two or-ders of magnitude more sensitive than LEP, and coveringsubstantial new phase space. In particular, at all stud-ied points, a new scalar with a coupling to the Z greaterthan 1% of that of a SM-higgs at the same mass wouldbe excluded or discovered at ILC-250. Preliminary stud-ies indicate that an ILC operating at 500 GeV could dis-cover or exclude such a scalar with a mass up to 350 GeV,even if the coupling is only one tenth of the coupling ofa would-be SM Higgs at the same mass [326]
13. CONCLUSION
In this report, we have reviewed the full panorama ofthe International Linear Collider project.This machine addresses compelling physics questions.In our quest to discover new interactions beyond theStandard Model, the couplings of the Higgs boson are5 (a) (b) (c)
FIG. 88: (a) The recoil mass distributions for various signals and all backgrounds after the cuts From [325]. (b) The 2 σ exclusion limits for the cross section scale factor k comparing the LEP and ILC-250 results. From [325]. (b) The 2 σ exclusionlimits for the cross section scale factor k comparing for ILC 250 and ILC-500. From [326]. the most obvious place to look, and the one place wheretoday we are not looking with sufficient power. The ILCwill supply the capabilities that we need to study theHiggs boson and other particles with the degree of preci-sion that is actually required to learn their secrets.The ILC provides a fully formed project proposal witha total cost estimate similar to that of the LHC, a moder-ate time scale for its construction, and well-tested tech-nologies for its accelerator and detector designs. TheILC is designed as a staged machine with its first stageat 250 GeV. Its design includes straightforward upgradepaths to extend this initial configuration. The full ILCmachine will be capable of running at center-of-mass en-ergies from the Z pole to 1 TeV, covering the productionthresholds of: Z , W W , Z -Higgs, top-quark, top-Higgsand Higgs pair production. The choice of energy can re-spond flexibly to new discoveries in particle physics, atthe LHC, at the ILC, or at other facilities.The ILC detectors are designed to meet the challengesof high precision. Taking advantage of the more benignenvironment of e + e − colliders, they are designed for per-formance on charged-particle tracking, heavy-flavor iden-tification, and calorimetry that improve on existing de-tectors by large factors. These are essential capabilitiesto confidently obtain the high-quality measurements thatwe seek.For first time in a collider for particle physics, the de-tectors will operate without any trigger system. Physicsanalyses and data-acquisition architecture will consider-ably benefit from this fact and consequently simplify withrespect to present and past experiments. The overallcomputing costs should be an order of magnitude smallerthan those for the LHC. The software and computingtools so far developed provide physics simulations anddetector studies that give solid predictions for the ILCperformance toward its physics goals. We have presentedthe results of those studies in this document.The ILC will use polarised electron and positronbeams. Beam polarisation brings both quantitative andqualitative advantages with respect to unpolarized e + e − colliders. Polarisation enhances signal reactions and al-lows the measurement of helicity-dependent observables,multiplying the physics output per unit of luminosity.It also allows suppression of backgrounds and accuratecontrol of systematic errors, improving the robustness ofhigh-precision measurements.The ILC machine is ready for construction. We havedescribed the detailed design of the ILC, explaining howthe performance of each component is supported by pro-totyping and, in most cases, by operational/industrialexperience.The physics program begins with a stage at 250 GeVin the center of mass. At this stage, each Higgs boson isproduced together with a Z boson at 110 GeV lab energythat serves to tag the event. This allows unambiguous,model-independent measurements of the total cross sec-tion for Higgs boson production and the branching ratiosfor Higgs boson decays. It also gives a tool for searchesfor exotic Higgs boson decays, including decays to invis-ible or partially visible final states.Measurements at the 250 GeV stage will improve cur-rent measurements of W boson couplings and SM quarkand lepton couplings by large factors beyond what is pos-sible at the HL-LHC.The simplicity of e + e − pair production allows the fullset of electroweak and Higgs processes at the ILC to becombined in a global fit based on an Effective Field The-ory description of modifications of the Standard Model.This framework is essentially model-independent withrespect to new physics. Within this framework, the250 GeV stage of the ILC will measure the Hbb cou-plings to 1%, the
HW W and
HZZ to 0.7%, and all otherimportant Higgs boson couplings to levels close to 1%.These are the levels of precision required to access newphysics beyond the reach of direct searches at HL-LHC.The first-stage ILC is intrinsically upgradable in en-ergy and luminosity. The accelerator and detectors aredesigned for operation up to a center of mass energyof 1 TeV. The technology, detector performance, andphysics for the 500 GeV stage has been described in de-6tail. All of the measurements discussed in the previousparagraphs benefit, with the uncertainties in Higgs bosoncouplings decreasing by a factor of 2. The 500 GeV stageoffers a program exploring the couplings of the top quarkand thus a second, independent, opportunity to probe fornew physics through precision measurement. It also of-fers the opportunity to search for pair-production of elu-sive particles produced in electroweak interactions thatare challenging to discover at the LHC. Running at the Z pole (ILC-GigaZ) is also possible. Essential observablesimplying lepton or quark left-right asymmetries can bemeasured with extremely high accuracy when combinedwith other measurements above the Z .The opportunities that the ILC gives to discover newphysics are robust, and the ILC measurements are im-provable as the accelerator moves from one energy stageto the next.We have compared the projected ILC performanceon Higgs boson couplings to those put forward forother colliders. The ILC will provide a significant—and necessary—step in precision beyond the HL-LHC. Anumber of other proposals for e + e − Higgs factories arenow under discussion. We have shown that none expectsa performance significantly superior to the ILC even atits 250 GeV stage. Also, no other proposal has been de-signed and costed at the level of a formal proposal. Only ILC is on the table today.Finally, the ILC laboratory will provide a base for fu-ture proposals of e + e − and γγ colliders based on ad-vanced high-gradient acceleration. The ILC laboratorythus can expect a long lifetime, beyond our current hori-zon, in which it will continue to explore the frontier offundamental physics.Come join us! It is time to make the InternationalLinear Collider a reality. Acknowledgements
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