A precise measurement of the top quark Yukawa coupling is of great
importance, since it may shed light on the mechanism of EWSB. We study the
prospects of such measurement during the first phase of the ILC at sqrt(s)=500
GeV, focusing in particular on recent theoretical developments as well as the
potential benefits of beam polarization. It is shown that both yield
improvements that could possibly lead to a measurement competitive with the
LHC.Comment: Invited talk at 2005 International Linear Collider Physics and
  Detector Workshop and Second ILC Accelerator Workshop, Snowmass, CO
  (Snowmass05) 3 pages, LaTeX, 3 eps figure

/Fermilab

Juste, A.

English

arXiv

A precise measurement of the top quark Yukawa coupling is of great importance, since it may shed light on the mechanism of EWSB. We study the prospects of such measurement during the first phase of the ILC at {radical}s = 500 GeV, focusing in particular on recent theoretical developments as well as the potential benefits of beam polarization. It is shown that both yield improvements that could possibly lead to a measurement competitive with the LHC

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2005 ALCPG & ILC Workshops - Snowmass, U.S.A.Towards a precise measurement of the top quark Yukawa coupling at theILCA. JusteFNAL, Batavia, IL 60510, USAA precise measurement of the top quark Yukawa coupling is of great importance, since it may shed light on themechanism of EWSB. We study the prospects of such measurement during the first phase of the ILC at√s = 500GeV, focusing in particular on recent theoretical developments as well as the potential benefits of beam polarization.It is shown that both yield improvements that could possibly lead to a measurement competitive with the LHC.1. INTRODUCTIONThe top quark Yukawa coupling (λt) is the largest coupling of the Higgs boson to fermions. A precise measurementof it is very important since the it may help unravel the secrets of the Electroweak Symmetry Breaking (EWSB)mechanism, in which the top quark could possibly play a key role. For mh < 2mt, a direct measurement of λtis possible via associated tt̄h production, both at the LHC and a future e+e− International Linear Collider (ILC).At the LHC, the expected accuracy [1] is δλt/λt ∼ 12 − 15% for mh ∼ 120 − 200 GeV, assuming an integratedluminosity of 300 fb−1. Existing feasibility studies at the ILC [2] predict an accuracy of δλt/λt ∼ 6 − 10% formh ∼ 120 − 190 GeV, assuming√s = 800 GeV and 1000 fb−1. However, currently the baseline design for theILC only contemplates a maximum center-of-mass energy of 500 GeV. Therefore, it is very relevant to explore theprospects of this measurement during the first phase of the ILC, especially in view of the limited accuracy expectedat the LHC: for a number of years, the combination of results from the LHC and ILC would yield the most precisedetermination of λt.A preliminary feasibility study at√s = 500 GeV was performed in Ref. [3], which we briefly overview here. Indeed,the measurement of λt at√s = 500 GeV is more challenging than at√s = 800 GeV. On the one hand, the reducedphase-space leads to a large reduction in σtt̄h (e.g. σBorntt̄h' 0.16(2.5) fb at √s = 500(800) GeV, for mh = 120 GeV).On the other hand, the cross section for many background processes is significantly increased. This analysis assumedmh = 120 GeV and focused on the tt̄h → (`νb)(jjb)(bb̄) decay channel (BR ∼ 30%). The dominant background istt̄jj, followed by tt̄Z, although other non-interfering backgrounds (e.g. W +W−) were also considered. Signal andbackgrounds were processed through a fast detector simulation. After basic preselection cuts, the signal efficiencywas found to be ' 50% and the S : B ' 1 : 100. In order to increase the sensitivity, a multivariate analysis using aNeural Network (NN) with 23 variables was performed. The final selection consisted on an optimized cut on the NNdistribution. Assuming an integrated luminosity of 1000 fb−1, the expected total number of signal and backgroundevents was 11 and 51, respectively, resulting in (δλt/λt)stat ' 33%. Based on previous experience [2], the additionof the fully hadronic decay channel was expected to ultimately lead to (δλt/λt)stat ' 23%. While this analysis isalready rather sophisticated, significant improvements are expected from e.g. the usage of a more efficient b-taggingalgorithm or a more optimal treatment of the kinematic information. In the next sections we discuss additionalsources of improvement which are currently under investigation.2. THE IMPACT OF RESUMMATION EFFECTSThe precise measurement of λt requires accurate theoretical predictions for σtt̄h. Currently, one-loop QCD andelectroweak corrections are available. However, at√s = 500 GeV and for mh ≥ 120 GeV, the kinematic regionALCPG0426FERMILAB-CONF-05-545-ETable I: Comparison of the Born and NLL σtt̄h for different scenarios regarding radiative effects in the initial state.(ISR,BS) σtt̄h (fb) (Born) σtt̄h (fb) (“NLL-improved”) Enhancement factor(off,off) 0.157(1) 0.357(2) 2.27(off,on) 0.106(1) 0.252(3) 2.38(on,on) 0.0735(8) 0.179(2) 2.44Eh (GeV)dσ/dEh (fb/GeV)√s=485 GeV00.0020.0040.0060.0080.010.0120.0140.0160.0180.02120 122 124 126 128 130 132 134 136 138 140Eh (GeV)dσ/dEh (fb/GeV)√s=500 GeV00.0050.010.0150.020.0250.03120 122 124 126 128 130 132 134 136 138 140Pe+σ Pe+Pe-/σ0ALR=0.44Pe-+1.0+0.8+0.6+0.4+0.2 0.0-0.2-0.4-0.6-0.8-1.000.511.522.53-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1Figure 1: Left and center: comparison of the Born (dashed) and NLL (solid) dσtt̄h/dEh for different values of√s, assumingm1St = 180 GeV and mh = 120 GeV. The dotted line indicates the value of Emaxh . Right: ratio of polarized to unpolarizedcross section for different values of (Pe− , Pe+).where the tt̄ system is non-relativistic dominates. As discussed in Ref. [4], in this regime Coulomb singularitiesare important and need to be resummed within the framework of the vNRQCD effective theory, leading to largeenhancements factors in the cross section relative to the Born level. At the ILC, because of ISR and beamstrahlung(BS), the event-by-event center-of-mass energy (√ŝ) will be lower than the nominal one, thus bringing the tt̄ systemdeeper into the non-relativistic regime. In order to compute the expected σtt̄h including these effects, the 11-foldBorn differential cross section for e+e− → tt̄h → W+bW−b̄h was multiplied by a K-factor defined as K(Eh,√ŝ) =(dσNLLtt̄h/dEh)/(dσBorntt̄h/dEh), where Eh stands for the Higgs boson energy in the e+e− rest-frame, and then foldedwith ISR and BS structure functions. The NLL differential cross section was kindly provided by the authors ofRef. [4]. Fig. 1(left and center) compares the Born (for off-shell top quarks) and NLL differential cross sectionsfor different values of√ŝ, assuming m1St = 180 GeV and mh = 120 GeV. The ratio of these two curves definesK(Eh,√ŝ) and can be significantly larger than 1, especially for low values of√ŝ. Since the NLL prediction isonly valid for Eh ≤ Emaxh (where Emaxh effectively corresponds to a cut on the top quark velocity in the tt̄ rest-frame of βt < 0.2), we currently set K(Eh,√ŝ) = 1 for Eh > Emaxh , although in practice, it should be possible touse K(Eh,√ŝ) = (dσO(αs)tt̄h/dEh)/(dσBorntt̄h/dEh). Table I compares the predicted Born and “NLL-improved” σtt̄hfor different scenarios, illustrating the large impact of radiative effects in the initial state. This underscores theimportance of being able to predict these effects to the percent level. While the impact of ISR cannot be reduced, itmight be possible to find an optimal operating point of the accelerator, as far as this measurement is concerned, interms of BS and total integrated luminosity. Finally, it is found that, for mh = 120 GeV, resummation effects canincrease σtt̄h by a factor of ∼ 2.4 with respect to the Born cross section, used in the previous feasibility study.3. THE IMPACT OF BEAM POLARIZATIONSo far, all feasibility studies of this measurement have assumed unpolarized beams. Currently, the baseline designfor the ILC only includes longitudinal electron beam polarization (|Pe− | ' 0.8). Positron beam polarization (|Pe+ | 'ALCPG04260.6) is considered as an option. The ratio of the polarized cross section (for arbitrary longitudinal beam polarization)(σPe−Pe+) to the unpolarized cross section (σ0) is given by σPe−Pe+/σ0 = (1 − Pe−Pe+)(1 − Peff ALR), wherePeff = (Pe− − Pe+)/(1 − Pe−Pe+) denotes the “effective polarization” and ALR is the “left-right asymmetry” ofthe process of interest [5]. Therefore, two potential enhancement factors can in principle be exploited: the first onerequires having both beams polarized, the second one requires ALR 6= 0 and a judicious choice of the signs of Pe− andPe+ in order to have Peff ALR < 0. In the case of SM tt̄h production, ALR ' 0.44, essentially independent of√s in therange ∼ 0.5 − 1.0 TeV. Assuming (ALR)SM , Fig. 1(right) shows the cross section enhancement factor as a functionof Pe+ , for different values of Pe− . The optimal (realistic) operating point would be (Pe− , Pe+) = (−0.8, +0.6),achieving an increase in σtt̄h by a factor of ' 2.1 with respect to the unpolarized case. Unfortunately, this choicedoes not help reduce the dominant background, which is increased by a similar factor. Nevertheless, the net result isstill an improvement in the statistical precision on λt by ∼ 45%, which would be an argument in favor of includingpositron polarization in the baseline design. For (Pe− , Pe+) = (−0.8, 0), only a modest increase in σtt̄h by a factor of∼ 1.3 would be achieved. It is important to realize that, in order to choose the sign of Pe− and Pe+ , it is necessaryto know the sign of ALR. Anomalous couplings in the ttγ and ttZ vertices could possibly lead to deviations in ALRfrom the SM prediction. Unfortunately, due to the limited precision in the measurement of the ttZ couplings [6],the LHC is not expected to provide any useful constraints on the sign of ALR. Therefore, at the ILC the first stepshould be to perform measurements of the polarized σtt̄ in order to determine the sign of ALR, and thus fix the signsof Pe− and Pe+ (the magnitudes should be largest possible). On the other hand, admittedly the measurement of λtrequires a percent-level and model-independent determination of the tt̄γ and tt̄Z couplings, which typically benefitsfrom changing the beam polarization. Therefore, it would be desirable to optimize the running strategy to maintainthe largest possible σtt̄h, needed for a precise measurement of λt, while meeting the precision goals for measurementsof top quark couplings.4. CONCLUSIONSWe have studied the prospects of a precise measurement of the top quark Yukawa coupling during the first phaseof the ILC. Taking into consideration an existing feasibility study, and the additional enhancement factors to σtt̄hdiscussed here, we anticipate a precision of (δλt/λt)stat ∼ 10% for mh = 120 GeV, assuming√s = 500 GeV and1000 fb−1.AcknowledgmentsThe author would like to thank André Hoang for useful discussions and for making available the NLL predictionsused in this study.References[1] G. Weiglein et al., arXiv:hep-ph/0410364.[2] A. Juste and G. Merino, arXiv:hep-ph/9910301; A. Gay, results presented at the 2nd ECFA/DECY Workshop,Saint Malo, France, April 12-15, 2002.[3] A. Juste, results presented at the Chicago Linear Collider Workshop, Chicago, USA, January 2002,http://www.pas.rochester.edu/~orr/justelc.pdf.[4] C. Farrell and A.H. Hoang, Phys. Rev. D 72, 014007 (2005) [arXiv:hep-ph/0504220]; C. Farrell and A.H. Hoang,these proceedings [arXiv:hep-ph/0506253].[5] G. Moortgat-Pick et al., arXiv:hep-ph/0507011.[6] U. Baur, A. Juste, L.H. Orr and D. Rainwater, Phys. Rev. D 71, 054013 (2005) [arXiv:hep-ph/0412021].ALCPG0426

Towards a precise measurement of the top quark Yukawa coupling at the ILC

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