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

By using the GRACE-Loop system, we calculate the full \(\mathcal{O}(\alpha)\) electroweak radiative corrections to the process \(e^+e^- \rightarrow e^+e^- \gamma\), which is important for future investigations at the International Linear Collider (ILC). With the GRACE-Loop system, the calculations are checked numerically by three consistency tests: ultraviolet finiteness, infrared finiteness, and gauge-parameter independence. The results show good numerical stability when quadruple precision is used. In the phenomenological results, we find that the electroweak corrections to the total cross section range from \(\sim -4\%\) to \(\sim -21\%\) when \(\sqrt{s}\) varies from \(250\) GeV to \(1\) TeV. The corrections also significantly affect the differential cross sections, which are a function of the invariant masses and angles and the final-particle energies. Such corrections will play an important role for the high-precision program at the ILC.