Pair production of scalar top quarks in polarized photon-photon collisions at ILC
A. Bartl, W. Majerotto, K. Mönig, A. N. Skachkova, N. B. Skachkov
备注:
34 pages, 34 EPS figures, ILC-NOTE-2007-036. v2 - another set of cuts was chosen. Submitted to the Proceedings of the 16-th International Seminar on High Energy Physics QUARKS-2010 (Kolomna, Russia, 6-12 June 2010). v3 - some typos corrected
We study pair production of scalar top quarks in polarized photon-photon collisions with the subsequent decay of the top squarks into b-quarks and charginos. We simulate this process by using PYTHIA6.4 for an electron beam energy 2E_beam =1000 GeV. A set of criteria for physical variables is proposed which leads to a good separation of stop signal events from top quark pair production being the main background. These criteria allow us to reconstruct the mass of the top squark provided that the neutralino mass is known.
The proposed International Linear Collider (ILC) is well-suited for discovering physics beyond the Standard Model and for precisely unravelling the structure of the underlying physics. The physics return of the ILC can be maximized by the use of polarized beams, in particular the simultaneous polarization of the e- and the e+ beam. Ongoing physics studies are accompanied by active R&D on the machine part for generating polarized beams and for measuring the polarization with high precision at the ILC. Some new results on the physics case and on the technical aspects of the polarization of both …
We study the top-quark pair production via polarized and unpolarized photon collisions at the International Linear Collider in the context of the littlest Higgs model with T-parity. We calculate the production cross section of the process $γγ\rightarrow t\bar{t}$ and find the effects can be more significant in the $- -$ polarized photon collision mode than in other collision modes, and the relative correction can be expected to reach about -1% in the favorable parameter space.
We study the possibility of using W pair production and leptonic decay of one of the W's at the ILC with polarized beams as a probe of the Littlest Higgs Model. We consider cross-sections, polarization fractions of the W's, leptonic decay energy and angular distributions, and left-right polarization asymmetry as probes of the model. With parameter values allowed by present experimental constraints detectable effects on these observables at typical ILC energies of 500 GeV and 800 GeV will be present. Beam polarization is further found to enhance the sensitivity.
At the International Linear Collider large beam polarization of both the electron and positron beams will enhance the signature of physics due to interactions that are beyond the Standard Model. Here we review our recently obtained results on a general model independent method of determining for an arbitary one-particle inclusive state the space-time structure of such new physics through the beam polarization dependence and angular distribution of the final state particle.
Non-standard scenarios described by effective interactions can manifest themselves indirectly, via corrections to the Standard Model cross sections. It should be desirable to identify at a given confidence level the source of such deviations among the different possible explanations. We here discuss the identification reach on gravity in extra dimensions from the four-fermion compositeness-inspired contact interactions and viceversa, using as basic observable the differential cross section of $e^+e^-\to\bar{f}f$ at the ILC, and emphasize the role of beams polarization in enhancing the identifi…
An updated study of measuring the W mass from a polarized threshold scan at ILC is presented with an emphasis on evaluating scan strategies that control experimental systematics. Highly longitudinally polarized beams of electrons and positrons such as are feasible at ILC offer significant advantages in terms of statistical power and in-situ control of background. Eventual experimental precision of around 2 MeV can be envisaged from this technique. Further work on both the accelerator design and theoretical uncertainties will likely be needed to take full advantage of this opportunity.
In view of the very precise measurements on fermion couplings which will be performed at ILC250 with polarized beams, there is emerging evidence that the LEP1/SLC measurements on these couplings are an order of magnitude too imprecise to match the accuracies reachable at ILC250. This will therefore severely limit the indirect sensitivity to new resonances and require revisiting the possibility to run ILC at the Z pole with polarized electrons. This work was done as a contribution to the ESU 2018-2020.
Numerous non-standard dynamics are described by contact-like effective interactions that can manifest themselves in electron-positron collisions only through deviations of the observables (cross sections, asymmetries) from the Standard Model predictions. If such a deviation were observed, it would be important to identify the actual source among the possible non-standard interactions as many different new physics scenarios may lead to very similar experimental signatures. We study the possibility of uniquely identifying the indirect effects of s-channel sneutrino exchange, as predicted by supe…
New heavy neutral gauge bosons Z' are predicted by many models of physics beyond the Standard Model. It is quite possible that Z's are heavy enough to lie beyond the discovery reach of the CERN Large Hadron Collider LHC, in which case only indirect signatures of Z' exchanges may emerge at future colliders, through deviations of the measured cross sections from the Standard Model predictions. We discuss in this context the foreseeable sensitivity to Z's of W^\pm-pair production cross sections at the e^+e^- International Linear Collider (ILC), especially as regards the potential of distinguishin…
One of the most-studied signals for physics beyond the standard model in the production of gauge bosons in electron-positron collisions is that due to the anomalous triple gauge boson couplings in the $Z γ$ final state. In this work, we study the implications of this at the ILC with polarized beams for signals that go beyond traditional anomalous triple neutral gauge boson couplings. Here we report a dimension-8 CP-conserving $Z γZ$ vertex that has not found mention in the literature. We carry out a systematic study of the anomalous couplings in general terms and arrive at a classification. We…
We study the possibility of fingerprinting a strongly interacting $W$ boson sector which is consistent with present day LHC searches at the ILC with longitudinal as well as transversely polarized electron and positron beams. We account for the final state interaction using a suitable Omnès formalism in terms of a plausible resonance description, and carry out thorough analyses of cross sections, asymmetries and angular distributions of the $W's$. We carry out a comparison with other extensions of the Standard Model, where heavy additional $Z'$ bosons arise naturally. We also consider the effec…
With high luminosity and energy at the ILC and clean SM backgrounds, the top-charm production at the ILC should have powerful potential to probe new physics. The littlest Higgs model with discrete symmetry named "T-parity"(LHT) is one of the most promising new physics models. In this paper, we study the FC processes $e^+e^-(γγ)\to t\bar{c}$ at the ILC in the LHT model. Our study shows that the LHT model can make a significant contribution to these processes. When the masses of mirror quarks become large, these two processes are accessible at the ILC. So the top-charm production at the ILC prov…
We study the effects of gluon radiation in top pair production and their decays for e+e- annihilation at the ILC. To achieve this we apply the POWHEG method and interface our results to the Monte Carlo event generator Herwig++. We consider a center-of-mass energy of 500GeV and compare decay correlations and bottom quark distributions before hadronization.
The International Linear e+e- Collider (ILC) could go into operation in the second half of the upcoming decade. Experimental analyses and theory calculations for the physics at the ILC are currently performed. We review recent progress, as presented at the LCWS06 in Bangalore, India, in the fields of Higgs boson physics and top/QCD. Also the area of loop calculations, necessary to achieve the required theory precision, is included.
Single top quark production at the ILC can be used to obtain a high precision measurements of the the Vtb CKM matrix element as well as the effective tbW coupling. We have calculated the QCD correction for the cross section in the context of an effective vector boson approximation. Our results show a 10% increase due to the strong interaction.
The physics case for studying top-quark physics at the International Linear Collider is well established. This summary places in context the top-quark physics goals, examines the current state-of-the art in understanding of the top-quark mass, and identifies some areas in which the study of the top-quark mass enhances our understanding of new techniques.
We study the effects of gluon radiation in top pair production and their decays for e+e- annihilation at the ILC. To achieve this we apply the POWHEG method and interface our results to the Monte Carlo event generator Herwig++. We consider a center-of-mass energy of \sqrt{s}=500 GeV and compare decay correlations and bottom quark and anti-quark distributions before hadronization.
We explore discrimination of two types of leptonic Yukawa interactions associated with Higgs triplet, $\bar L^c_L ΔL_L$, and with $SU(2)$ singlet doubly charged scalar, $\bar e_R^c k^{++} e_R$. These interactions can be distinguished by measuring the effects of doubly charged scalar boson exchange in the $e^+ e^- \to \ell^+ ell^-$ processes at polarized electron-positron colliders. We study a forward-backward asymmetry of scattering angular distribution to estimate the sensitivity for these effects at the ILC. In addition, we investigate prospects of upper bounds on the Yukawa couplings by com…
I will briefly review the status of higher-order calculations for top-quark observables, comment on the need for improvements, discuss some of the recent theoretical advances, and present a few examples to highlight the role of top-quark observables in searches for signals of physics beyond the Standard Model.
We study the effects of unparticle physics in the pair productions of top quarks at the LHC and ILC. By considering vector, tensor and scalar unparticle operators, as appropriate, we compute the total cross sections for pair production processes depending on scale dimension $d_{\U}$. We find that the existence of unparticles would lead to measurable enhancements on the SM predictions at the LHC. In the case of ILC this may become two orders of magnitude larger than that of SM, for smaller values of $d_\U$, a very striking signal for unparticles.
We consider the possibility of fingerprinting the presence of heavy additional Z' bosons that arise naturally in extensions of the standard model such as E_6 models and left-right symmetric models, through their mixing with the standard model Z boson. By considering a class of observables including total cross sections, energy distributions and angular distributions of decay leptons we find significant deviation from the standard model predictions for these quantities with right-handed electrons and left-handed positrons at \sqrt{s}=800 GeV. The deviations being less pronounced at smaller cent…
In this paper we study the effect of new physics contributions to the top quark pair production ($t\bar{t}$) in a possible future linear collider, such as the International Linear Collider (ILC). The use of a dimension-six gauge invariant effective operator approach allows to compare the prospected results at the ILC with the current ones obtained at the Large Hadron Collider (LHC), both in neutral and charged current processes. We also prove that the use of specific observables, together with a combination of measurements in different polarized beam scenarios and with different center-of-mass…
We explore the effects of neutrino and electron mixing with exotic heavy leptons in the process e^+e^-\to W^+W^- within E_6 models. We examine the possibility of uniquely distinguishing and identifying such effects of heavy neutral lepton exchange from Z-Z' mixing within the same class of models and also from analogous ones due to competitor models with anomalous trilinear gauge couplings (AGC) that can lead to very similar experimental signatures at the e^+e^- International Linear Collider (ILC) for \sqrt{s}=350, 500 GeV and 1 TeV. Such clear identification of the model is possible by using a…
The topcolor-assisted technicolor (TC2) model predicts some light pseudo goldstone bosons (PGBs), which may be accessible at the LHC or ILC. In this work we study the pair productions of the charged or neutral PGBs at the LHC and ILC. For the productions at the LHC we consider the processes proceeding through gluon-gluon fusion and quark-antiquark annihilation, while for the productions at the ILC we consider both the electron-positron collision and the photon-photon collision. We find that in a large part of parameter space the production cross sections at both colliders can be quite large co…
We investigate the weak electric and magnetic dipole moments of top quark-Z boson interactions at the Large Hadron Collider (LHC) and the International Linear Collider (ILC). Their vanishingly small magnitude in the Standard Model makes these couplings ideal for probing New Physics interactions and for exploring the role of top quarks in electroweak symmetry breaking. In our analysis, we consider the production of two top quarks in association with a Z boson at the LHC, and top quark pairs mediated by neutral gauge bosons at the ILC. These processes yield direct sensitivity to top quark-Z boso…
We investigate the anomalous $W^+W^-γ$ couplings through the process $e^-e^+\,\rightarrow\,ν_e\barν_eγ$ for unpolarized and polarized electron (positron) beams at the International Linear Collider. We give the 95$\%$ Confidence Level limits on the anomalous couplings with and without the systematic uncertainties for various values of center-of-mass energies and the integrated luminosities. We show that the obtained limits on the anomalous couplings through the process $e^-e^+\,\rightarrow\,ν_e\barν_eγ$ can highly improve the current experimental limits.
In the littlest Higgs model with T-parity, we studied the contributions of the new particles to the top-quark pair production via $e^{+}e^{-}$ collision at the International Linear Collider. We calculated the top-quark pair production cross section and found this process can generate significantly relative correction. The result may be a sensitive probe of the littlest Higgs model with T-parity.
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.
The process of top quark pair production at the ILC with subsequent decays of one of the top quarks to a charged Higgs boson and b-quark is considered. The charged Higgs decays to tau leptons whose polarization is the opposite to those coming from W bosons. This difference is reflected in the energy distributions of the tau decay products in the top quark rest frame, which can be reconstructed at the ILC using the recoil mass technique. We present an analysis including spin correlations, backgrounds, ISR/FSR and beamstrahlung, and show that a fit of the shape of the pion energy spectrum yields…
We calculate the electroweak and QCD corrections to W-W+ -> tt and ZZ -> tt. We also consider the interplay of these corrections with the effect of anomalous interactions that affect the massive weak bosons and the top. The results at the VV level fusion are convoluted with the help of the effective vector boson approximation to give predictions for a high energy e+e- collider.
The top-color assisted technicolor (TC2) mode predicts the existence of a pair of charged top-pions $π^{\pm}_t$. In this paper, we study the production of the charged top-pions pair $π^{\pm}_t$ at next generation $γγ$ colliders. The results show that the production rates can reach the level of $10^2$ fb with reasonable parameter space. With a large number of events and the clean background, the charged top-pion should be observable at the $γγ$ colliders. Therefore, our studies can help us to search for charged top-pion, and furthermore, to test the TC2 model.
We investigated top quark effects on virtual photon structure functions by pQCD. We include the top quark mass effects on the virtual photon structure function with the quark parton model and with the operator product expansion up to the next-to-leading order in QCD. We also consider the threshold effect on the running coupling constant in the calculation to the effective photon structure function with a matching condition. The numerical calculations are investigated in the kinematical region expected at the future international linear collider.
In topcolor-assisted technicolor models (TC2) the hitherto unconstrained lepton flavor mixing induced by the new gauge boson $Z'$ will lead to the lepton flavor violating productions of $τ\bar μ$, $τ\bar e$ and $μ\bar e$ in photon-photon collision at the proposed International Linear Collider (ILC). Through a comparative analysis of these processes, we find that the better channels to probe the TC2 is the production of $τ\bar μ$ or $τ\bar e$ which occurs at a much higher rate than $μ\bar e$ production due to the large mixing angle and the large flavor changing coupling, and may reach the detec…
The littlest Higgs model with T-parity (LHT) has new flavor-changing (FC) couplings with the Standard Model (SM) quarks, which do not suffer strong constraints from electroweak precision data. So these FC interactions may enhance the cross sections of some flavor-changing neutral-current (FCNC) processes. In this work, we study the FC top-charm associated productions via $e^{-}γ$ collision at the ILC. We find that the cross sections are sensitive to the mirror quark masses. With reasonable values of the parameters, the cross sections may reach the detectable level and provide useful informatio…
We have studied the associated production processes of a neutral top-Higgs in the topcolor assisted technicolor model with a pair of heavy quarks in γγcollisions at the International Linear Collider (ILC). We find that the cross section for t\bar{t}h_t in γγcollisions is at the level of a few fb with the c.m. energy \sqrt{s}=1000 GeV, which is consistent with the results of the cross section of t\bar{t}H in the standard model and the cross section of t\bar{t}h in the minimal supersymmetric standard modeland the little Higgs models. It should be distinct that hundreds of to thousands of h_t per…
Top quark decays are of particular interest as a mean to test the standard model (SM) predictions, both for the dominant ($t\to b+W$) and rare decays ($t\to q+W, cV, cVV,cϕ^0,bWZ$). As the latter are highly suppressed, they become an excellent window to probe the predictions of theories beyond the SM. In particular, in this paper, we evaluate the corrections from new physics to the CKM-suppressed SM top quark decay $t\to q+W$ ($q=d,s$), both within the effective lagrangian approach and the MSSM and we discuss the perspectives to probe those predictions at the ILC.
Measurement of the top-Yukawa coupling is important to understand the fermion mass generation mechanism and dynamics of electroweak symmetry breaking. We discuss the top quark anomalous couplings which can be described by higher dimensional operators. We investigate the process $e^-e^+ \to W^-W^+ν\barν\to t \bar t ν\barν$ to study the contribution of the anomalous top-Higgs coupling to the cross section. The effect of the dimension-six top-Higgs interaction on the cross section can be a few hundred percent greater than the SM prediction. Such a large effect can be measured at the International…
The large top quark mass suggests that the top plays a pivotal role in Electroweak symmetry-breaking dynamics and, as a result, may have modified couplings to Electroweak bosons. Hadron colliders can provide measurements of these couplings at the ~10% level, and one of the early expected triumphs of the International Linear Collider is to reduce these uncertainties to the per cent level. In this article, we propose the first direct measurement of the Standard Model W-t-b coupling at the ILC, from measurements of t tbar-like signals below the t tbar production threshold. We estimate that the IL…
We study neutralino production at the linear collider with the subsequent two-body decays ~chi^0_i -> ~chi^0_n Z^0 and Z^0 -> l^+ l^-, with l=e, mu, tau, or Z^0 -> q q- with q=c,b. We show that transverse electron and positron beam polarizations allow the definition of unique CP observables. These are azimuthal asymmetries in the distributions of the final leptons or quarks. We calculate these CP asymmetries and the cross sections in the Minimal Supersymmetric Standard Model with complex higgsino and gaugino parameters mu and M_1. For final quark pairs, we find CP asymmetries as large as 30%. …
I discuss the calculation of cross sections for processes with six and eight fermions in the final state, contributing to single-top production and associated top-Higgs production at a linear collider. I describe the schemes for the treatment of finite decay widths implemented in the matrix element generator O'Mega and give a numerical comparison for single-top production. In the case of single top production, after reducing vector boson fusion backgrounds by appropriate cuts, the effect of including the full six fermion final state amounts to 2-5%. In associated top-Higgs production, non-reso…
In this work, we analyze three dominant single SM-like Higgs boson production processes in the left-right twin Higgs model (LRTHM): the Higgs-strahlung (HS) process $e^{+}e^{-}\rightarrow Zh$, the vector boson fusion (VBF) process $e^{+}e^{-}\to ν\barνh$ and the associate production with top pair process $e^{+}e^{-}\to t\bar{t}h$ for three possible energy stages of the International Linear Collider (ILC), and compared our results with the expected experimental accuracies for various accessible Higgs decay channels. The following observations have been obtained: (i) In the reasonable parameter …
We study pair production of scalar top quarks in e+e- collisions with the subsequent decay of the top squarks into b-quarks and charginos. We simulate this process by using PYTHIA6.4 for the beam energy 2Ebeam = 350, 400, 500, 800, 1000 GeV. A set of criteria for physical variables is proposed, which provides good separation of stop signal events from top quark pair production being the main background. These criteria allow us to reconstruct the mass of the top squark with an integrared luminosity of 1000 1/fb provided that the neutralino mass is known.
In the present work the $Z^\prime tc$ coupling is bounded by using the current experimental data on the $D^{0}-\bar{D^{0}}$ meson-mixing system. It is found that the strength associated to this coupling is less than $5.75\times 10^{-2}$. The single top production through the $e^+e^-\to Z^\prime\to tc$ process at the $Z^\prime$ boson resonance is studied and we found that around $10^7$ $tc$ events will be expected at the International Linear Collider. For the $Z^\prime\to tc$ decay, we predict a branching ratio of $10^{-2}$.
Full one-loop electroweak-corrections for an $e^-e^+\rightarrow t \bar{t}$ process associated with sequential $t\rightarrow b μν_μ$ decay are discussed. At the one-loop level, the spin-polarization effects of the initial electron and positron beams are included in the total and differential cross sections. A narrow-width approximation is used to treat the top-quark production and decay while including full spin correlations between them. We observed that the radiative corrections due to the weak interaction have a large polarization dependence on both the total and differential cross sections.…
Prospects to search for a new massless neutral gauge boson, the paraphoton, in e+ e- collisions at center-of-mass energies of 0.5 and 1 TeV are studied. The paraphoton naturally appears in models with abelian kinetic mixing. A possible realistic model independent lowest order effective Lagrangian contains magnetic interactions of the paraphoton with the Standard Model fermion fields. These interactions are proportional to the fermion mass and grow with energy, with however very weak paraphoton couplings to ordinary matter. At the ILC, a potentially interesting process to search for the parapho…
In this work we study a scalar field dark matter model with mass of the order of 100 MeV. We assume dark matter is produced in the process $e^-+e^+\to ϕ+ϕ^*+γ$, that, in fact, could be a background for the standard process $e^-+e^+\to ν+\barν+γ$ extensively studied at LEP. We constrain the chiral couplings, $C_L$ and $C_R$, of the dark matter with electrons through an intermediate fermion of mass $m_F=100$ GeV and obtain $C_L=0.1(0.25)$ and $C_R=0.25(0.1)$ for the best fit point of our $χ^2$ analysis. We also analyze the potential of ILC to detect this scalar dark matter for two configurations…
The assumption of a new symmetry provides a nice explanation of the existence of dark matter and an elegant way to avoid the electroweak constraints. This symmetry often requires the pair production of new particles at colliders and it guarantees that cascade decays down to the lightest particle give rise to missing energy plus jets and leptons. For a long time, supersymmetry with the conserved R-parity was the only candidate for such signals. However, any new physics with this type of new symmetry may show up with similar signals and the discrimination between different models at the LHC is q…
Recently proposed idea of unparticles arising due to a scale invariant sector in the theory can give rise to effective operators with different Lorentz structures. We show that by using the different polarization options at the future linear e+e- colliders, the nature of these effective operators can be easily understood. The unique feature of a complex phase in the propagator of the unparticle can also be understood uniquely for the different spins by exploiting the initial beam polarizations at the International Linear Collider (ILC).
A study of top quark production at the future International Linear Collider, ILC, with a centre-of-mass energy of 500 GeV is presented. The emphasis is put on determining the sensitivity to physics beyond the Standard Model. The analysis has been carried out with a full simulation of the ILD detector. Both, the forward-backward asymmetry and the left-right asymmetry can be determined to a precision of about 1% to 1.5%. The analysis points out an ambiguity which arises in case of the production of top-quarks with left-handed helicity.
A short overview about the potential of polarized beams at future colliders is given. In particular the baseline design for polarized beams at the ILC is presented and the physics case for polarized $e^-$ and $e^+$ is discussed. In order to fulfil the precision requirements spin tracking from the source to the interaction point is needed. Updates concerning the theoretical calculations as well as their implementation in simulation codes are reported.
We report on the feasibility of the direct measurement of the top Yukawa coupling g_t at the International Linear Collider (ILC) during its first phase of operation with a center-of-mass energy of 500 GeV. The signal and background models incorporate the non-relativistic QCD corrections which enhance the production cross section near the t-tbar threshold. The e+e- -> t tbar H signal is reconstructed in the 6-jet + lepton and the 8-jet modes. The results from the two channels are combined. The background processes considered are e+e- -> t bbar W- / tbar b W+ (which includes e+e- -> t tbar), e+e…
We investigate the effect of top trilinear operators in t tbar production at the ILC. We find that the sensitivity to these operators largely surpasses the one achievable by the LHC either in neutral or charged current processes, allowing to probe new physics scales up to 4.5 TeV for a centre of mass energy of 500 GeV. We show how the use of beam polarisation and an eventual energy upgrade to 1 TeV allow to disentangle all effective operator contributions to the Ztt and gamma tt vertices.
We study the pair production of scalar top quarks in e+e- collisions with the subsequent decay of the top squarks into b-quarks and charginos. We simulate this process using PYTHIA6.4 for beam energies 2E_beam = 350, 400, 500, 800, 1000 GeV. Proposing a set of criteria we obtain a good separation of the signal stop events from top quark pair production which is the main background. The number of stop production events obtained with the proposed cuts for different energies is calculated for an integrated luminosity of 1000 1/fb. We propose a method to reconstruct the mass of the top squark, pro…
The International Linear Collider (ILC) will be able to precisely measure the electroweak couplings of the top in e+e- -> tt~. We compare the limits which can be achieved at the ILC with those which can be obtained in tt~gamma$ and tt~Z production at the Large Hadron Collider (LHC).
Precise predictions for an $e^+e^-\rightarrow t\bar{t}$ cross-section are presented in the energy region from 400 GeV to 800 GeV. Cross-sections are estimated including the beam-polarization effects with full $\mathcal{O}(α)$, and also with the effects of the initial-state photon emission. A radiator technique is used for the initial-state photon emission up to two-loop orders. In this investigation, a weak correction is defined as the full electroweak corrections without the initial-state photonic corrections. As a result, it is determined that the total cross-section of a top quark pair-prod…
The average charged hadron multiplicity in the $e^+e^-$ events with the primary $t\bar{t}$-pair at the collision energy 500 GeV, as well as the average multiplicity of charged hadrons from the top quark are calculated in QCD to be $86.7 \pm 1.11$ and $41.0 \pm 0.54$, respectively.
Precise predictions for an $e^+e^-\rightarrow t\bar{t}$ cross section are presented at an energy region from 400 GeV to 800 GeV. Cross sections are estimated including the beam-polarization effects with full $\mathcal{O}(α)$, and also with effects of the initial-state photon emission. A radiator technique is used for the initial-state photon emission up to two-loop order. A weak correction is defined as the full electroweak corrections without the initial-state photonic corrections. As a result, it is obtained that the total cross section of a top quark pair-production receives the weak correc…