Muon Colliders: Opening New Horizons for Particle Physics
Kenneth Long, Donatella Lucchesi, Mark Palmer, Nadia Pastrone, Daniel Schulte, Vladimir Shiltsev
MMuon Colliders:Opening New Horizons for Particle Physics
K. Long, D. Lucchesi, M. Palmer, N. Pastrone, D. Schulte, V.ShiltsevAugust 3, 2020
Abstract
Particle colliders have arguably been the most important instruments forparticle physics over the past 50 years. As they became more powerful,they were used to push the frontier of our knowledge into previously un-charted territory. The LHC, the highest energy collider to date, at whichthe Higgs boson was discovered, is a prime example. To continue alongthe road into the
Terra Promissa beyond the Standard Model requirescolliders with energy reach even greater than that of the LHC. Beams ofmuons offer enormous potential for the exploration of the energy frontier.Since the muon is a fundamental particle, its full energy is available incollisions in contrast to protons which are composed of quarks and gluons.However, muon beams decay rapidly, which presents a special challengefor a collider. Recent research indicates that the technologies required toovercome this challenge are within our grasp and may offer a cost-effectiveand energy-efficient option to continue our explorations. A new interna-tional collaboration is forming to bring together the diverse expertise andcomplementary capabilities from around the world to realise the muoncollider as the next-generation energy-frontier discovery machine.
Evaluation of future high energy particle physics facilities has traditionally beenbased on three criteria: scientific potential; technical construction and financialrequirements; and flexibility for further upgrades and developments [1]. Themost recent update of the European Strategy for Particle Physics has added animportant new requirement—next generation facilities should meet very highecological and environmental standards and, in particular, they must be energyefficient [2].Colliding two particle beams, each with energy E , allows the explorationof center-of-mass energy scales up to √ s = 2 E . Since they were developed inthe 1960s, colliders have been built in a variety of types, shapes, and sizes.Today, colliders represent the largest and most expensive facilities for funda-mental science research [3]. To fulfill our aspirations of an order-of-magnitudeincrease in the center-of-mass energy in particle collisions requires a paradigmshift from the traditional and well-established technologies of proton-proton andelectron-positron colliders. 1 a r X i v : . [ phy s i c s . acc - ph ] J u l he concept of colliding beams of positively and negatively charged muonsoriginated in the late 1960s [4]. Two fundamental issues drive the design of amuon collider—the short lifetime of the muon and the challenge of producingbright muon beams. Detailed design studies and technological research [5, 6,7, 8, 9] have demonstrated the feasibility of using muon beams in a multi-TeVcollider that addresses each of the criteria set out in the 2020 update of the Eu-ropean Strategy for Particle Physics. Muons can be accelerated and collided inrings without suffering from the large synchrotron radiation losses that limit theperformance of electron-positron colliders. This allows a muon collider to usethe traditional and well-established accelerator technologies of superconductinghigh-field magnets and RF cavities. Furthermore, unlike protons, where thecollision energy is shared among the constituent quarks and gluons, muons arepoint-like particles that deliver their entire energy √ s to the collision - thusprobing significantly higher energy scales ( ∼ × higher, depending on the pro-cess) than protons colliding with the same beam energy. Finally, the electricpower efficiency of muon colliders (defined as the collider’s annual integratedluminosity, (cid:82) Ldt , divided by the facility’s annual energy use) increases withenergy. Thus, above approximately √ s = 2 TeV, a muon collider is expected tobe the most energy-efficient choice for the exploration of the energy frontier asshown in Figure 1. This would be the first time unstable particles are ussed ina collider. A muon collider operating at an energy >
10 TeV would enable direct searchesfor new particles over a wide range of unexplored masses [10]. Figure 2 comparesthe center-of-mass energy √ s µ at a muon collider to that at a proton-protonmachine, √ s p , required to directly produce a pair of new heavy particles ofmass M ∼ √ s µ / ∼ cm − s − , it would be possible toproduce enough double and triple-Higgs events to make a direct measurement ofthe trilinear and quadrilinear self-couplings of the Higgs boson, thus providinga unique and precise determination of the shape of the Higgs potential. Figure3 shows how a typical double-Higgs event would appear in the detector when2igure 1: Annual integrated luminosity, (cid:82) Ldt , per Terawatt-hour of electricpower consumption, (cid:82)
P dt , plotted as a function of the center-of-mass energyfor a variety of particle colliders, as taken from reference [3]. This ratio isshown as a function of center-of-mass energy for: the Muon Collider (MC) (solidred circles); the LHC, both at present and after its luminosity upgrade (solidblack diamonds); the Future Circular electron-positron Collider (FCC-ee, solidmagenta circles) assuming experiments at two collision points; the InternationalLinear Collider (ILC, solid blue circles), the Compact Linear Collider (CLIC,solid cyan circles), the High Energy LHC (HE-LHC, solid magenta diamonds);and the Future Circular proton-proton Collider (FCC-hh, solid green diamonds).The effective energy reach of hadron colliders (LHC, HE-LHC and FCC-hh) isapproximately a factor of 7 lower than that of a lepton collider operating at thesame energy per beam. 3igure 2: Energy reach of muon-muon collisions: the energy at which the protoncollider cross-section equals that of a muon collider (taken from reference [11]).The plot compares the pair-production cross-sections for heavy particles withmass M at approximately half the muon collider energy √ s µ /
2. The dashedyellow line assumes comparable processes for muon and proton production, whilethe continuous blue line accounts for the possible QCD enhancement of theproduction rates at a proton-proton collider.both Higgs bosons decay to b and anti-b quark jet pairs.The detector must be capable of operating in the presence of the beam-induced background produced tens of meters upstream of the interaction pointalong the beam line by the interactions between the decay products of the muonbeams and the machine elements. The particle types (mainly photons, electronsand neutrons), flux, angular, and energy distributions of the background alldepend strongly on the exact details of the machine lattice. This requires thedesign of the machine-detector interface to be optimized along with the colliderdesign at a given energy. Two tungsten shielding cones (nozzles), emanatingfrom the collision point and inserted inside the tracker detector volume, mitigatethe effects of the high levels of beam-induced background close to the beampipe. The experiment, in particular the tracking system shown in Figure 3,requires detectors with performance that exceeds the present state of the art,e.g., being capable of few tens of ps timing resolution to reject out-of-timebeam-induced background [13]. Detector designs must be developed furtherto enable simultaneous measurements of the position, time and energy of theparticles originating from the collision point, as well as to exploit new artificialintelligence on-detector data handling and reconstruction tools.4igure 3: A typical double Higgs boson event simulation produced at a center-of-mass energy of 3 TeV. Each Higgs boson is identified by its decay to a b andanti-b quark jet pair. Grey lines show the path in the tracking detectors, wherecharged particles produced by each b-jet are enclosed in a yellow cone. Thered dots represent the jet shower energy deposition inside the calorimeter in theouter region of the detector. 5
Main Collider Parameters, Systems and Syn-ergies
As noted above, the short lifetime of the muon and the provision of a muonsource with sufficient brightness represent particular challenges for the realisa-tion of a muon collider. Rapid acceleration to high energies increases the lifetimeof the muons in proportion to their energy—a lifetime of 21 ms is achieved at1 TeV. A possible layout for a 6–14 TeV center-of-mass energy muon colliderwith a luminosity O (10 cm − s − ) is shown in Figure 4. A high-power protondriver produces a dense beam that is further compressed in an accumulator anda compressor ring. The proton beam is directed onto a target where positive andnegative pions are produced that subsequently decay into positive and negativemuons. The muons are captured in two beams, depending on their charge, thatare subsequently cooled using the novel ionization-cooling technique and thenaccelerated in several stages before being injected into the collider ring. Thecooling system is essential to reduce the large initial phase space by a factor ofmore than 10 to that needed for a practical collider. Without such cooling, theluminosity would be too small by several orders of magnitude.The proposed ionization-cooling technique is very fast and uniquely appli-cable to muons because of their minimal interaction with matter. Ionizationcooling involves passing the muon beam through some material in which themuons lose energy via the ionization energy-loss mechanism. Both transverseand longitudinal momentum are reduced in this process. Longitudinal momen-tum only is then restored by subsequent acceleration in RF cavities. The com-bination of energy loss and re-acceleration causes a net reduction in the phasespace occupied by the beam, hence cooling the beam. The process is repeatedmany times to achieve a large cooling factor–see Figure 5.Theoretical studies and numerical simulations [7] have shown that, with re-alistic parameters for the cooling hardware, ionization cooling is expected toreduce the phase-space volume occupied by the initial muon beam sufficientlyto provide acceptable luminosity in a collider. A complete cooling channel wouldconsist of a series of tens of cooling stages, each reducing the 6D phase-spacevolume by a roughly a factor of 2 (see Figure 5). The ionization cooling method,though relatively straightforward in principle, presents challenges in its practi-cal implementation. These challenges include the suppression of RF breakdownnormal-conducting RF cavities immersed in strong magnetic fields. The in-ternational Muon Ionization Cooling Experiment (MICE) at the RutherfordAppleton Laboratory (UK) has recently demonstrated effective, O (10%), re-duction of the transverse phase-space volume (emittance) of 140 MeV/c muonspassing through a prototype ionization cooling-channel cell using both lithium-hydride and liquid-hydrogen absorbers within a magnetic guiding-and-focusinglattice with peak fields of 4 T [14]. In the final stages of a cooling channel for acollider, relatively small aperture solenoid magnets having the highest possiblefields, tens of Tesla, will be required to deliver beams of the quality required fora multi-TeV collider. 6 cceleratorRingMuon Collider >10TeV CoM~10km circumference µ - µ + p Decay& µ BunchingChannel µ CoolingChannel Low Energy µ Acceleration µ Injector IP 1IP 2
Figure 4: Schematic layout of a 10 TeV-class muon collider complex. Themuon injector systems include the proton driver, a high power target systemwith capture solenoid for the pions generated by the proton interactions withthe target, a pion decay channel where muons are collected and subsequentlybunched together, a muon ionization cooling channel that provides cooling forboth positive and negative muon beams by more than 5 orders of magnitude,and a low energy muon accelerator stage that would deliver beams with energiesup to 100 GeV. From the injector, each species of muon beam is transferred intoa high energy accelerator complex that can take the beams to the multi-TeVenergies required. Finally, the beams will be transferred to a smaller colliderring whose circumference is optimized for luminosity performance. A 10 TeV-class collider ring is anticipated to support at least 2 detector interaction regionsfor the physics program. 7igure 5: Ionization cooling-channel scheme. 200 MeV muons are born when4 GeV protons hit a solid target. The muons are collected and sent into a coolingchannel where they lose energy in lithium hydride (LiH) absorbers. The lostenergy is restored when the muons are accelerated in the longitudinal directionin RF cavities. The superconducting solenoids magnets confine the beam withinthe channel and radially focus the beam at the absorbers.8enter of mass energy √ s (TeV) .126 3 14Circumference (km) 0.3 4.5 14Interaction points 1 2 2Average luminosity (10 cm − s − ) 0.008 1.8 40Integrated luminosity/detector (ab − /year) 0.001 0.18 4Time between collisions ( µs ) 1 15 47Cycle repetition rate (Hz) 1 5 5Energy spread (rms, % ) 0.004 0.1 0.1Bunch length (rms, mm) 63 5 1IP beam size ( µ m) 75 3.0 0.6Dipole design field (T) 10 10 15Proton driver beam power (MW) 4 4 1Beam power in collider (MW) 0.08 5.3 20.2Table 1: Tentative parameters of variants of future high-energy muon colliders,including the µ + µ − Higgs factory. A detailed design of a 14 TeV center-of-massmuon collider design is not yet complete and the numbers shown here are aprojection [15].Technological challenges also arise in other systems required to deliver highquality beams to the collision point in a muon collider. High-gradient normaland superconducting RF systems are required to accelerate the beams rapidlybefore the beams decay. Superconducting dipole magnets capable of providing10 T to 15 T magnetic fields are required to keep the collider ring as small aspossible, thereby maximizing the number of muon collisions before muon decaydissipates the beams. In the accelerator ring, fast-ramping magnets will haveto be cycled several times a second, which requires that the energy stored inthese magnets must be recovered with very high efficiency to preserve the powerefficiency of the accelerator complex.Muon decays produce intense neutrino fluxes that are concentrated primar-ily in line with the straight sections of the collider ring. A small fraction of theseneutrinos interact with the rock and other matter as they emerge at the sur-face of the Earth, thus producing ionizing radiation. The neutrino interactionrate in the vicinity of the surface rises linearly with energy. The impact of thisneutrino-induced radiation can be mitigated, for example, by adding a verticalperturbation in the collider orbit [16]. A further reduction in the neutrino-induced radiation would be obtained if the emittance of the muon beam wasreduced so that the required luminosity could be obtained using a significantlysmaller number of muons. A novel muon production scheme, LEMMA, hasrecently been proposed in which muon pairs are produced through e + e − annihi-lation just above the production threshold when 45 GeV positron beam strikesa solid target [17]. This scheme might allow beams to be produced with muchlower current but much higher phase-space density, thus delivering the sameluminosity but with significantly reduced neutrino-induced radiation.9omprehensive overviews of the techniques that have been developed to ad-dress the issues relevant for the construction of a muon collider can be foundin references [7, 8]. These publications, and the documents to which they refer,describe the significant progress that has been made and summarise the feasibil-ity studies that have been carried out to demonstrate that a muon collider witha √ s >
10 TeV can be built with current or emerging technology (see Table 1).The development of an energy-frontier muon collider has elements that havegreat synergy with other efforts in the field. For instance, the need for the de-velopment of high-field magnets parallels the ongoing R&D program for veryhigh energy proton-proton colliders [18]. The development of a high bright-ness muon source would also benefit other scientific endeavours. In particular,muons from a proton driver-based source would provide high purity and preciselycharacterized neutrino beams for long- and short-baseline neutrino experiments[19, 20, 21].
The LHC luminosity upgrade will extend the physics program at the world’shighest energy collider to about 2040. It is possible to envision a path to-wards an energy-frontier muon collider in Europe by the mid- to late 2040s.The technically-limited plan starts with an initial four year development phaseto establish baseline designs for a 3 TeV collider with a luminosity of ∼ · cm − s − and a >
10 TeV collider with a luminosity of ∼ · cm − s − .The discovery potential of the >
10 TeV machine would be competitive to orexceed that of any other energy frontier collider option being evaluated at themoment.The resulting baseline designs will allow to evaluate the cost scale and risksof a muon collider and define the muon production, cooling, and accelerationtest facility (or facilities) as a basis to decide on the future of the project. Theinitial phase of the program would be followed by a second phase of roughly 6years to construct and operate the test facility. The collider design would alsobe optimized during this period. The results of this second phase would lay thefoundations for a decision to move forward into the third four-year phase duringwhich a full technical design would be developed. The construction of the muoncollider itself is estimated to require a further 10 years.The focus of the technical development towards successful implementationof a muon collider will be on key systems that can reduce the cost of the colliderand to increase its power efficiency and performance. Laboratories in Europe,Asia, the US, and around the world have sufficient expertise to deliver elementsof the program. These laboratories are joining together to form the interna-tional collaboration required to explore the various options and to develop anintegrated design concept that encompasses the physics, the detectors and theaccelerator. This effort will bring the outstanding features of the muon colliderto bear on the exploration of the
Terra Promissa of new phenomena that arebeyond reach of the LHC. 10 eferences [1] J.Irvine, B.Martin, ”CERN: Past performance and future prospects: III.CERN and the future of world high-energy physics”, Research Policy, 13(5),247 (1984).[2] 2020 Update of the European Strategy for Particle Physics https://home.cern/sites/home.web.cern.ch/files/2020-06/2020UpdateEuropeanStrategy.pdf , see also the EPPSU ”Physics briefingbook”, arXiv:1910.11775 (2019).[3] V.Shiltsev, F.Zimmermann, ”Modern and future colliders”,arXiv:1901.06150 [physics.acc-ph] (2019).[4] F.F.Tikhonin, ”On the Effects with Muon Colliding Beams”, JINR ReportP2-4120 (Dubna, 1968, in Russian); G.Budker, ”Accelerators and CollidingBeams”, Proceedings of the 7th Int. Conf. Part. Accel. Physics (Yerevan,1969), 1, 33 (1970).[5] C.Ankenbrandt, et al., ”Status of muon collider research and developmentand future plans”, Physical Review Special Topics-Accelerators and Beams,2 (8), 081001 (1999).[6] S.Geer, ”Muon colliders and neutrino factories”, Annual Review of Nuclearand Particle Science, 59, 347 (2009).[7] R.B. Palmer, ”Muon colliders”, Rev. Accel. Sci. Tech. 7, 137 (2014).[8] M.Boscolo, J.P. Delahaye, M.Palmer, ”The future prospects of muon collid-ers and neutrino factories”, Reviews of Accelerator Science and Technology,10, 189 (2019).[9] The Muon Accelerator Program, https://map.fnal.gov/ ; see alsoJINST Special Issue on Muon Accelerators for Particle Physics https://iopscience.iop.org/journal/1748-0221/page/extraproc46 .[10] V. Barger, M. Berger, J. Gunion, T. Han, ”Particle physics opportunities at µ + µ −−