Constraining capability of $Z \gamma h$ production at the ILC

Higgs boson couplings with gauge bosons are probed through $e^-e^+ \rightarrow Z \gamma h$ in an effective Lagrangian framework. For this study the beam polarization facility at the ILC along with the typical center-of-mass energy of 500 GeV is considered. The reach of the ILC with an integrated luminosity of 300 fb$^{-1}$ in the determination of $CP$-conserving parameters is obtained. Sensitivity of the probe of each of these couplings in the presence of other couplings is investigated. The most influential coupling parameters are $\bar c_W=-\bar c_B$. Other parameters of significant effect are $\bar c_{HW}$ and $\bar c_{HB}$. A detailed study of the various kinematic distributions represents possibilities to disentangle the effect of some of these couplings.