Full \(\mathcal{O}(\alpha)\) electroweak radiative corrections to \(e^+e^- \rightarrow t \bar{t} \gamma\) with GRACE-Loop

We present the full \(\mathcal{O}(\alpha)\) electroweak radiative corrections to the process \(e^+e^- \rightarrow t \bar{t} \gamma\) at the International Linear Collider (ILC). The computation is performed with the help of the GRACE-Loop system. We present the total cross-section and the top quark forward-backward asymmetry (\(A_{FB}\)) as a function of the center-of-mass energy and compare them with the process \(e^+e^- \rightarrow t \bar{t}\). We find that the value of \(A_{FB}\) in \(t \bar{t} \gamma\) production is larger than \(A_{FB}\) in \(t\bar{t}\) production. It is an important result for the measurement of the top quark forward-backward asymmetry at the ILC. Applying a structure function method, we also subtract the QED correction to gain the genuine weak correction in both the \(\alpha\) scheme and the \(G_{\mu}\) scheme (\(\delta_{W}^{G_{\mu}}\)). We obtain numerical values for \(\delta_{W}^{G_{\mu}}\) which are changing from 2% to -24% when we vary the center-of-mass energy from 360 GeV to 1 TeV.