One-loop QCD and electroweak corrections to $t\bar{t}Z^0$ production at an $e^+e^-$ linear collider

We study the impact of the full ${\cal O}(\alpha_{s})$ QCD and ${\cal O}(\alpha_{ew})$ electroweak (EW) radiative corrections to the $e^+e^- \to t \bar t Z^0$ process in the standard model (SM), and investigate the dependence of the lowest-order(LO), one-loop QCD and EW corrected cross sections on colliding energy $\sqrt{s}$. The LO, QCD and EW corrected spectrums of the invariant mass of $t\bar t$-pair and the distributions of the transverse momenta of final top-quark and $Z^0$-boson are presented. The numerical results show that the one-loop QCD correction enhances the LO cross section, but the EW one-loop correction generally suppresses the LO cross section with our chosen parameters. In the case of $m_H=120 GeV$, the QCD relative corrections can reach 43.16% when $\sqrt{s} = 500 GeV$, while the EW relative corrections have the values of -9.24%, -4.36% and -5.81%, when $\sqrt{s} = 500 GeV$, $800 GeV$, 1.2 TeV$, respectively.