We study the $h gamma Z$ coupling, which is a loop induced coupling in the Standard Model (SM), to probe new physics. In a global fit based on the SM Effective Field Theory, measurement of the SM $h gamma Z$ coupling can provide a very useful constraint, in particular for the precise determination of $hZZ$ and $hWW$ couplings. At the International Linear Collider (ILC), there are two direct ways to study the $h gamma Z$ coupling: one is to measure the branching ratio of the $h to gamma Z$ decay and the other to measure the cross section for the $e^+e^- to h gamma$ process. We have performed a full simulation study of the $e^+e^- to h gamma$ process at the 250 GeV ILC, assuming 2 ab$^{-1}$ data collected by the International Large Detector (ILD). The expected 1$sigma$ bound on the effective $hgamma Z$ coupling ($zeta_{AZ}$) combining measurements of the cross section for $e^+e^- to h gamma$ followed by $h to b bar{b}$ and the $h to gamma Z$ branching ratio is $-0.0015<zeta_{AZ}<0.0015$. The expected significance for the signal cross section in the fully hadronic $h to WW^*$ channel is 0.09 $sigma$ for beam polarizations of $P(e^-,e^+)=(-80%,+30%)$.
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