aa r X i v : . [ h e p - ph ] N ov Electroweak Physics at the ILC
G. Weiglein
IPPP, Department of Physics, Durham University, Durham DH1 3LE, U.K.E-mail:
Abstract.
Some aspects of electroweak physics at the International Linear Collider (ILC)are reviewed. The importance of precision measurements in the Higgs sector and in top-quarkphysics is emphasized, and the physics potential of the GigaZ option of the ILC is discussed.It is shown in particular that even in a scenario where the states of new physics are so heavythat they would be outside of the reach of the LHC and the first phase of the ILC, the GigaZprecision on the effective weak mixing angle may nevertheless allow the detection of quantumeffects of new physics.
1. Introduction
The International Linear Collider (ILC) is a proposed electron–positron collider whose designis being addressed in the context of the Global Design Effort [1]. The ILC has been agreed ina world-wide consensus to be the next large experimental facility in high-energy physics (seeRef. [2] and references therein). The Reference Design Report for the ILC has been issued earlierthis year [1], and the Engineering Design Report is currently in preparation.The baseline design of the ILC foresees a first phase of operation with a tunable energy of upto about 500 GeV and polarised beams. Possible options include running at the Z-boson polewith high luminosity (GigaZ) and running in the photon–photon, electron–photon and electron–electron collider modes. The physics case of the ILC with centre-of-mass energy of 400–500 GeVrests on high-precision measurements of the properties of the top quark at the top threshold, theunique capability of performing a comprehensive programme of precision measurements in theHiggs sector, which will be indispensable to reveal the nature of possible Higgs candidates, thegood prospects for observing the light states of various kinds of new physics in direct searches,and the sensitivity to detect effects of new physics at much higher scales by means of high-precision measurements [3].The baseline configuration furthermore foresees the possibility of an upgrade of the ILC to anenergy of about 1 TeV. The final choice of the energy and further possible machine and detectorupgrades will depend on the results obtained at the LHC and the first phase of the ILC.The information on TeV scale physics obtainable at the electron–positron collider ILC willbe complementary to the one from the proton–proton collider LHC [4,5]. While the discovery ofnew particles often requires access to the highest possible energies, disentangling the underlyingstructure calls for highest possible precision of the measurements. Quantum corrections areinfluenced by the whole structure of the model. Thus, the fingerprints of new physics oftenonly manifest themselves in tiny deviations. While in hadron collisions it is technically feasibleto reach the highest centre-of-mass energies, in lepton collisions (in particular electron-positroncollisions) the highest precision of measurements can be achieved. High-precision physics at theLC is made possible in particular by the collision of point-like objects with exactly defined initialconditions, by the tunable collision energy of the ILC, and by the possibility of polarising theILC beams. Indeed, the machine running conditions can easily be tailored to the specific physicsprocesses or particles under investigation. The signal-to-background ratios at the ILC are ingeneral much better than at the LHC. In contrast to the LHC, the full knowledge of the momentaof the interacting particles gives rise to kinematic constraints, which allow reconstruction of thefinal state in detail. The ILC will therefore provide very precise measurements of the propertiesof all accessible particles. Direct discoveries at the ILC will be possible up to the kinematiclimit of the available energy. Furthermore, the sensitivity to quantum effects of new physicsachievable at the ILC will in fact often exceed that of the direct search reach for new particlesat both the LHC and the ILC.The ILC can deliver precision data obtained from running at the top threshold, from fermionand boson pair production at high energies, from measurements in the Higgs sector and ofpossible other new physics. Furthermore, running the ILC in the GigaZ mode yields extremelyprecise information on the effective leptonic weak mixing angle at the Z-boson resonance, sin θ eff ,and the mass of the W boson, M W (the latter from running at the WW threshold). The GigaZrunning can improve the accuracy in the effective weak mixing angle by more than an order ofmagnitude. The precision of the W mass would improve by at least a factor of two comparedto the expected accuracies at the Tevatron and the LHC. Comparing these measurements withthe predictions of different models provides a very sensitive test of the theory [6], in the sameway as many alternatives to the Standard Model (SM) have been found to be in conflict withthe electroweak precision data in the past.In the following, some examples of electroweak physics at the ILC are briefly discussed.
2. Higgs physics at the ILC
The high-precision information obtainable at the ILC will be crucial for identifying the natureof new physics. For instance, once one or more Higgs candidates are detected, a comprehensiveprogramme of precision measurements will be necessary to reveal the properties of the newstate(s) and to determine the underlying physics. The mass of the Higgs boson can be determinedat the ILC at the permille level or better, Higgs couplings to fermions and gauge bosons cantypically be measured at the percent level, and it will be possible to unambiguously determinethe quantum numbers in the Higgs sector. Indeed, only the ILC may be able to discern whethera Higgs candidate observed at the LHC is the Higgs boson of the SM or a Higgs-like (possiblycomposite) scalar tied to a more complex mechanism of mass generation. The verification ofsmall deviations from the SM may be the path to decipher the physics of electroweak symmetrybreaking. The experimental information from the ILC will be even more crucial if the mechanismof electroweak symmetry breaking in nature is such that either Higgs detection at the LHC maybe difficult or the Higgs signal, while visible, would be hard to interpret.A possible scenario giving rise to non-standard properties of the Higgs sector is the presence oflarge extra dimensions, motivated for instance by a “fine-tuning” and “little hierarchy” problemof supersymmetric extensions of the SM. A popular class of such models comprise those in whichsome or all of the SM particles live on 3-branes in the extra dimensions. Such models inevitablyrequire the existence of a radion (the quantum degree associated with fluctuations of the distancebetween the 3-branes or the size of the extra dimension(s)). The radion has the same quantumnumbers as a Higgs boson. As a consequence, there will in general be a mixing between theHiggs boson(s) and the radion. Since the radion has couplings that are very different from thoseof the SM Higgs boson, the physical eigenstates will have unusual properties corresponding to amixture of the Higgs and radion properties. In such a situation the ILC could observe both theHiggs and the radion and measure their properties with sufficient accuracy to experimentallyestablish the Higgs-radion mixing effects.f no clear Higgs signal has been established at the LHC, it will be crucial to investigatewith the possibilities of the ILC whether the Higgs boson has not been missed at the LHCbecause of its non-standard properties. This will be even more the case if the gauge sector doesnot show indications of strong electroweak symmetry breaking dynamics. The particular powerof the ILC is its ability to look for e + e − → ZH in the inclusive e + e − → ZX missing-massdistribution recoiling against the Z boson. Even if the Higgs boson decays in a way that isexperimentally hard to detect or different Higgs signals overlap in a complicated way, the recoilmass distribution will reveal the Higgs-boson mass spectrum of the model. The total Higgs-strahlung cross section will be measurable with an accuracy of about 2.5% for a Higgs bosonwith a mass of about 120 GeV. Should no fundamental Higgs boson be discovered, neither at theLHC nor at the ILC, high-precision ILC measurements will be a direct probe of the underlyingdynamics responsible for particle masses. The LHC and the ILC are sensitive to different gaugeboson scattering channels and yield complementary information [5].
3. Top and electroweak precision physics
The ILC is uniquely suited for carrying out high-precision top-quark physics. The mass of thetop quark, m t , is a fundamental parameter of the electroweak theory. It is by far the heaviest ofall quark masses and it is also larger than the masses of all other known fundamental particles.The large value of m t gives rise to a large coupling between the top quark and the Higgs bosonand is furthermore important for flavour physics. The top quark could therefore provide awindow to new physics. The correct prediction of m t will be a crucial test for any fundamentaltheory. The top-quark mass also plays an important role in electroweak precision physics, asa consequence in particular of non-decoupling effects being proportional to powers of m t . Aprecise knowledge of m t is therefore indispensable in order to have sensitivity to possible effectsof new physics in electroweak precision tests [7].The ILC measurements at the top threshold will reduce the experimental uncertainty on thetop-quark mass to the level of 100 MeV or below [3, 8], i.e., more than an order of magnitudebetter than at the Tevatron [9] and the LHC [4,10], and would allow a much more accurate studyof the electroweak and Higgs couplings of the top quark. A precision of m t significantly betterthan 1 GeV will be necessary in order to exploit the prospective precision of the electroweakprecision observables. In particular, an experimental error on m t of 0.1 GeV induces anuncertainty in the theoretical prediction of M W and the effective weak mixing angle, sin θ eff , of1 MeV and 0 . × − , respectively [7], i.e., below the anticipated experimental error of theseobservables.The impact of the experimental error on m t is even more pronounced in Higgs physics. Ineach model where the Higgs-boson mass is not a free parameter but predicted in terms of theother model parameters (as, e.g., in supersymmetry) the leading top-quark loop contributioninduces a correction to the Higgs-boson mass of the form∆ m h ∼ G µ N C C m t . (1)Here G µ is the Fermi constant, N C is the colour factor, and the coefficient C depends on thespecific model. Taking the Minimal Supersymmetric Standard Model (MSSM) as an example(including also the scalar top contributions and the appropriate renormalisation) N C C is givenfor the light CP -even Higgs boson mass by N C C = 3 √ π sin β log (cid:18) m ˜ t m ˜ t m t (cid:19) . (2)Here m ˜ t , denote the two masses of the scalar tops. An LHC precision of δm t = 1 GeVleads to an uncertainty of the prediction for m h induced by δm t of also about 1 GeV. TheLC accuracy on m t , on the other hand, will yield a precision of the Higgs-mass predictionof about 0 . δm exp , LHC h ≈ . m t is mandatory in order to obtaina theoretical prediction for m h with the same level of accuracy as the anticipated experimentalprecision on the Higgs-boson mass.
4. Electroweak precision observables in the MSSM
The high-precision measurement of the effective leptonic weak mixing angle at the Z-bosonresonance, sin θ eff , at GigaZ provides an extremely sensitive probe of quantum effects of newphysics [6]. In Ref. [12] precision physics at the Z-boson resonance has been discussed in thecontext of the MSSM, based on state-of-the-art theoretical predictions. It has been analysed inparticular whether the high accuracy achievable at the GigaZ option of the ILC would providesensitivity to indirect effects of SUSY particles even in a scenario where the (strongly interacting)superpartners are so heavy that they escape detection at the LHC.
100 200 300 400 500 600 700 800 900 1000 M χ ± ~ [GeV] s i n θ e ff SM (M H SM = M h MSSM ) ± σ para-ILC (sin θ eff ) exp = today ± σ ILC squarks & gluinos: M
Q,U,D =6 (M
Q,U,D ) SPS ; A u,d =6 (A u,d ) SPS ; m g =6 (m g ) SPS~~ sleptons, neutralinos & charginos: M
L,E =scale (M
L,E ) SPS ; A τ =scale (A τ ) SPS ; M =scale (M ) SPS scale = (SUSY mass scale varied)
SPS1a’ ± σ para-ILC Figure 1.
Theoretical prediction for sin θ eff in the SM and the MSSM (including prospectiveparametric theoretical uncertainties) compared to the experimental precision at the ILC withGigaZ option. An SPS1a ′ inspired scenario is used, where the squark and gluino mass parametersare fixed to 6 times their SPS 1a ′ values. The other mass parameters are varied with a commonscalefactor.In Fig. 1 a scenario with very heavy squarks and a very heavy gluino is considered. It is basedon the values of the SPS 1a ′ benchmark scenario [13], but the squark and gluino mass parametersare fixed to 6 times their SPS 1a ′ values. The other masses are scaled with a common scalefactor except M A , the mass of the CP -odd Higgs boson, which is kept fixed at its SPS 1a ′ value.In this scenario the strongly interacting particles are too heavy to be detected at the LHC, while,depending on the scale-factor, some colour-neutral particles may be in the ILC reach. Fig. 1shows the prediction for sin θ eff in this SPS 1a ′ inspired scenario as a function of the lighterchargino mass, m ˜ χ ± . The prediction includes the parametric uncertainty, σ para − ILC , induced bythe ILC measurement of m t , δm t = 100 MeV, and the numerically more relevant prospectivefuture uncertainty on ∆ α (5) had, δ (∆ α (5) had) = 5 × − [14]. The MSSM prediction for sin θ eff is compared with the experimental resolution with GigaZ precision, σ ILC = 0 . M H SM = M MSSM h )is also shown, applying again the parametric uncertainty σ para − ILC .Despite the fact that no coloured SUSY particles would be observed at the LHC in thisscenario, the ILC with its high-precision measurement of sin θ eff in the GigaZ mode couldresolve indirect effects of SUSY up to m ˜ χ ± < ∼
500 GeV. This means that the high-precisionmeasurements at the ILC with GigaZ option could be sensitive to indirect effects of SUSY evenin a scenario where SUSY particles have neither been directly detected at the LHC nor the firstphase of the ILC with a centre of mass energy of up to 500 GeV.
Acknowledgements
The author thanks the authors of Refs. [2, 5, 12] for collaboration on the topics discussed in thispaper and G. Moortgat-Pick for interesting discussions concerning Sect. 4. Work supportedin part by the European Community’s Marie-Curie Research Training Network under contractMRTN-CT-2006-035505 ‘Tools and Precision Calculations for Physics Discoveries at Colliders’(HEPTOOLS). [1] See .[2] T. Akesson et al.,
Eur. Phys. J.
C 51 (2007) 421, hep-ph/0609216.[3] A. Djouadi et al. [ILC Global Design Effort and World Wide Study], arXiv:0709.1893 [hep-ph];J.A. Aguilar-Saavedra et al. [ECFA/DESY LC Physics Working Group Collaboration],arXiv:hep-ph/0106315;T. Abe et al. [American Linear Collider Working Group Collaboration], in
Proc. of Snowmass 2001 , ed.N. Graf, arXiv:hep-ex/0106055;K. Abe et al. [ACFA Linear Collider Working Group Coll.], arXiv:hep-ph/0109166; see: lcdev.kek.jp/RMdraft/ .[4] ATLAS Collaboration,
Detector and Physics Performance Technical Design Report , CERN/LHCC/99-15(1999), see: atlasinfo.cern.ch/Atlas/GROUPS/PHYSICS/TDR/access.html ;CMS Collaboration,
Physics Technical Design Report, Volume 2. CERN/LHCC 2006-021 , see: cmsdoc.cern.ch/cms/cpt/tdr/ .[5] [LHC / ILC Study Group], G. Weiglein et al.,
Phys. Rept. (2006) 47, hep-ph/0410364.[6] S. Heinemeyer, T. Mannel and G. Weiglein, hep-ph/9909538;R. Hawkings and K. M¨onig,
EPJdirect
C 8 (1999) 1. hep-ex/9910022;J. Erler, S. Heinemeyer, W. Hollik, G. Weiglein and P. Zerwas,
Phys. Lett.
B 486 (2000) 125,hep-ph/0005024;U. Baur, R. Clare, J. Erler, S. Heinemeyer, D. Wackeroth, G. Weiglein and D. Wood, hep-ph/0111314;S. Heinemeyer, W. Hollik and G. Weiglein,
Phys. Rept. (2006) 265, hep-ph/0412214.[7] S. Heinemeyer, S. Kraml, W. Porod and G. Weiglein,
JHEP (2003) 075, hep-ph/0306181;S. Heinemeyer and G. Weiglein,
In the Proceedings of 2005 International Linear Collider Workshop(LCWS 2005), Stanford, California, 18-22 Mar 2005, pp 0401 , hep-ph/0508168;G. Weiglein,
Nature , 613 (2004).[8] A. Hoang et al.,
Eur. Phys. Jour.
C 3 (2000) 1, hep-ph/0001286;M. Martinez, R. Miquel,
Eur. Phys. Jour.
C 27 (2003) 49, hep-ph/0207315.[9] Tevatron Electroweak Working Group, hep-ex/0703034.[10] M. Beneke et al., hep-ph/0003033.[11] G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich and G. Weiglein,
Eur. Phys. J.
C 28 (2003) 133,hep-ph/0212020;S. Heinemeyer, W. Hollik and G. Weiglein,
Eur. Phys. J.
C 9 (1999) 343, hep-ph/9812472.[12] S. Heinemeyer, W. Hollik, A.M. Weber and G. Weiglein, arXiv:0710.2972 [hep-ph].[13] B. Allanach et al.,
Eur. Phys. J.
C 25 (2002) 113, hep-ph/0202233;the definition of the MSSM parameter for the SPS points can be found at ∼ georg/sps/ ;J. Aguilar-Saavedra et al., Eur. Phys. J.