Study of the $h \gamma Z$ coupling at the ILC

We studied the $e^+e^- \to h \gamma$ process at the full simulation level, using a realistic detector model to study the feasibility to constrain the SM effective field theory (SMEFT) $h \gamma Z$ coefficient, $\zeta_{AZ}$, at the ILC. Assuming International Large Detector (ILD) operating at 250 GeV ILC, it is shown that the $e^+e^- \to h\gamma$ process is much more difficult to observe than naively expected if there is no BSM contribution. We thus put upper limits on the cross section of this process. The expected combined 95% C.L. upper limits for full polarisations $(P_{e^-}, P_{e^+})=(-100\%, +100\%)$ and $(+100\%, -100\%)$ are $\frac{\sigma_{h \gamma}^{L}}{\sigma_{S M}^{L}}<5.0$ and $\frac{\sigma_{h \gamma}^{R}}{\sigma_{S M}^{R}}<61.9$, respectively. The resultant 95% C.L. limit on $\zeta_{AZ}$ is $-0.020<\zeta_{A Z}<0.003$.