SUSY-QCD Effects in Top Quark Pair Production in Association with a Gluon at the ILC

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1 Commun. Theor. Phys. 64 (2015) Vol. 64, No. 2, August 1, 2015 SUSY-QCD Effects in Top Quark Pair Production in Association with a Gluon at the ILC ZHANG Yan-Ming ( ) and LIU Ning ( ) Institute of Theoretical Physics, Henan Normal University, Xinxiang , China (Received March 16, 2015; revised manuscript received May 4, 2015) Abstract Given the null results of searches for new physics at the LHC, we investigate the one-loop effects SUSY QCD in the process e + e t tg at the ILC in Minimal Supersymmetric Standard Model (MSSM). We find that the relative SUSY-QCD corrections to the cross section of e + e t tg can maximally reach 6.5%(3.2%) at the ILC with s = 1000 GeV when m t 1 = GeV and m g = 500(1500) GeV. PACS numbers: Ha, Bx, Ej Key words: top quark, ILC, QCD 1 Introduction In the Standard Model (SM), top quark is the heaviest fermion and hence has the strongest coupling to the Higgs boson. Therefore, it is expected to play an important role in understanding the electroweak symmetry breaking mechanism. [1] Since the top quark was discovered at the Tevatron in 1995, [2 3] it has been widely studied by the theorists and experimentalists in the past decades. At hadron colliders, such as Tevatron and LHC, the top quark are mainly produced in pair via the QCD interactions. The Tevatron experiments collected a data sample of about 12 fb 1 in Run-I and Run-II. With the running of LHC at 7 TeV and 8 TeV, more data has been accumulated and allows more precise studies of the top quark than ever before. So far, most measurements of its properties are consistent with the SM predictions. Given all the relevant experiments, the new physics in the top quark sector has been pushed into a corner. For example, the LHC results of searches for the same-sign dileptons set a strong constraint on the cross section of the samesign top pair production; [4 6] No excess observed in the t t resonant searches has excluded a new mediator with mass M X 1 TeV; [7 9] The bounds on the top quark FCNC couplings have been greatly improved at the LHC; [10 15] The recent Higgs data has given a strong bound on the CP-violating top-higgs couplings; [16 19] The measured spin correlation and polarization in t t production strongly disfavored the non-sm top quark interactions. [20 24] In this situation, the precise measurements of various top quark productions and decays will be the only way to find the footprint of new physics. Due to the clean environment and expected high luminosity, the ILC will be an ideal place to explore the new physics through the quantum effect. [25 26] At the ILC, the production mechanism for top quark pairs is changed from the strong to the electro-weak interactions. This will be a closer step to explore the electro-weak symmetry breaking. [27] The leading order process e + e t t is induced by the interactions of t tγ/z, which can be measured at the one percent level of the ILC. [28] Therefore, the high order calculations for the top quark processes are needed to meet the experimental precision at the ILC. The SM/Supersymmetric QCD and electroweak corrections to e + e t t, [29 31] e + e t tγ [32] and e + e /γγ t tz [33] productions have been calculated. In Refs. [34 35], the author also investigates the process e + e t tg in the presence of anomalous chromo-magnetic t tg coupling at the ILC. In this work, we will calculate the process e + e t tg at one-loop level in Minimal Supersymmetric Standard Model (MSSM). In MSSM, the supersymmetric particles, in particular stop and gluino, can alter the process e + e t tg through quantum effect. Given the recent great progress of the LHC experiments, it is meaningful to examine the SUSY effect in e + e t tg under the experimental constraints. This paper is organized as follows: In Sec. 2 we give a description of analytical calculations for the process e + e t tg. In Sec. 3 we give the numerical results and some discussions. Finally, we make a short summary in the last section. 2 A Description of Analytical Calculations Assuming that the contributions of Higgs couplings to light fermions are neglectable, we generate Feynman diagrams in Mathematica automatically with package FeynArts-3.9. [36] At the tree-level, the Feynman diagrams Supported by the National Natural Science Foundation of China (NNSFC) under Grant Nos , , and , by Specialized Research Fund for the Doctoral Program of Higher Education under Grant No and by the Startup Foundation for Doctors of Henan Normal University under Grant No wlln@mail.ustc.edu.cn c 2015 Chinese Physical Society and IOP Publishing Ltd

2 No. 2 Communications in Theoretical Physics 167 of the process e + e t tg are shown in Fig. 1. It is convenient to denote the momenta of the initial and the final states for this process as follows: e + (q 1 ) + e (q 2 ) t(q 3 ) + t(q 4 ) + g(q 5 ). (1) The tree-level differential cross section can be expressed as dσ tree = 1 M tree 2 dφ 3, (2) 4 spins,polar where M tree is the sum of the tree-level Feynman amplitudes and dφ 3 is the three-particle phase space element. In our calculation, the Feynman amplitudes are generated automatically by FeynArts and the t Hooft Feynman gauge are adopted. Subsequently, we simplify the amplitudes and generate the Fortran code for the cross section computation with FormCalc-8.3. [37] Fig. 1 Tree-level Feynman diagrams for the process e + e t tg. Fig. 2 Feynman diagrams for SUSY-QCD corrections to the process e + e t tg. In Fig. 2, we display the Feynman diagrams of the oneloop SUSY-QCD corrections to the process e + e t tg. We adopt the dimensional regularization to isolate all the ultraviolet divergences (UV) in the virtual loop corrections and remove them with the on-mass-shell renormalization scheme. [38] The relevant renormalization constants are available for calculating the top quark SUSY- QCD self-energy. After the renormalization, we numerically check and find that the result is ultraviolet-finite. Moreover, there are no infrared (IR) singularities in the one-loop integrals. In our numerical calculation, we use LoopTools2.8 [39] to evaluate the loop integrals. Finally, the complete one-loop SUSY-QCD corrected production cross section of the process e + e t tg can be expressed as σ tot = σ tree + σ tot = σ tree + σ vir = σ tree (1 + δ tot ), (3) where δ tot σ tot /σ tree is the relative one-loop SUSY- QCD correction. 3 Numerical Results and Discussions In our numerical calculation, the SM parameters are chosen as [41] α(m Z ) = 1/ , α s (m Z ) = GeV, m Z = GeV, m W = GeV, m e = GeV, m t = GeV. (4) After the electroweak symmetry breaking, two CPeven Higgs bosons (h, H), one CP-odd Higgs boson (A) and the charged Higgs bosons (H ± ) are predicted in the MSSM. The mass of the lighter CP-even Higgs boson (m h ) is bounded to be smaller than M Z at tree level. However, the Higgs mass can be lifted by the large radiative corrections from the heavy stop sector at one-loop level. The leading part of the stop loop corrections can be written as [40] δm 2 h( t) 3m 4 [ t 2π 2 v 2 sin 2 log m t 1 β m 2 + X2 t t 2m t 1 ( )] 1 X2 t, (5) 6m t 1 where X t A t µ cot β is the mixing parameter of the left-handed and right-handed stops. Obviously, to obtain a 125 GeV m h, one needs the heavy stop masses or a sizable stop mixing parameter X t. In our work, we calculate the Higgs mass with the package FeynHiggs [42] and impose the LEP, Tevatron, and LHC constraints on the MSSM Higgs sector by using the package HiggsBounds [43] Since only stop mass and gluino mass are involved in the process e + e t tg, we decouple the first two generation squark soft masses (M q1,2 ), electroweak

3 168 Communications in Theoretical Physics Vol. 64 gaugino masses (M 1,2 ), slepton soft masses (M l1,2,3 ) and pseudo-scalar mass (M A ) by setting them a common mass M SUSY = 2 TeV. We vary the stop parameters to achieve 123 GeV< m h < 127 GeV: 1 tan β 60, 300 GeV (M Q3, M U3 ) 2 TeV, 2 TeV A t 2 TeV. (6) It should be mentioned that a very light stop has been tightly constrained by the LHC searches for direct stop pair production in the simplified models or with the specific assumption of branching ratios. [44 45] So we set the lower limit for stop soft mass as 300 GeV in our calculation. In order to tag the hard jet in the final states, we take E g > 0.5 GeV. The phase-space integral is numerically performed by using the Monte Carlo routine VEGAS coded in FormCalc. Fig. 3 The relative one-loop SUSY-QCD corrections δ tot versus the stop mass m t 1 for m g = 500 GeV, 1000 GeV, 1500 GeV at the ILC with the center-of-mass energy s = 500 GeV. Fig. 4 The relative one-loop SUSY-QCD corrections δ tot versus the center-of-mass energy s at the ILC for m t = GeV and m g = 500 GeV, 1000 GeV, 1500 GeV, respectively. In Fig. 3, we present the relative one-loop SUSY-QCD corrections versus the stop mass m t 1 for m g = 500 GeV, 1000 GeV, 1500 GeV respectively at the ILC with the center-of-mass energy s = 500 GeV. We can see that the relative one-loop SUSY-QCD corrections δ tot decreases when the stop and gluino become heavy, which indicates that the one-loop SUSY-QCD effects of the MSSM in the process e + e t tg decouple in heavy sparticle mass limit. For m g = 500 GeV, 1000 GeV, 1500 GeV, δ tot can maximally reach 1.75%, 1.24%, and 1.03% respectively at m t 1 = GeV. In Fig. 4, we display the relative one-loop SUSY-QCD corrections δ tot versus the center-of-mass energy s at the ILC for m t = GeV and m g = 500 GeV, 1000 GeV, 1500 GeV, respectively. From Fig. 4, we can see that the relative correction δ tot decreases with the increase of the center-of-mass energy s due to the s-channel suppression. For m g = 1500 GeV, the relative correction δ tot can still reach 3.2% at s = 1 TeV. Considering the projected high precision in top pair production, [25] we may expect that such a deviation may be observed at the ILC. 4 Summary In this paper, we have investigated the complete oneloop SUSY QCD effects to the associated production of the top pair with a gluon at the ILC. We have found that the relative SUSY-QCD corrections to the cross section of e + e t tg can maximally reach 6.5%(3.2%) at the ILC with s = 1000 GeV when m t 1 = GeV and m g = 500(1500) GeV.

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