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.