Associated production of SM Higgs with a photon in type-II seesaw models at the ILC

We consider the production of a single Standard Model (SM) Higgs boson ($h^0$) in association with a photon at the future Linear collider (LC) in the context of a type-II seesaw model. The type-II seesaw model extends the SM particle content by adding one triple Higgs where its Higgs coupling is a key parameter of the scalar potential triggering the electroweak symmetry-breaking mechanism in the SM. It is a well motivated model since it provides neutrino masses and mixing. The LC presents a particularly interesting possibility to probe Higgs couplings due to the clean beams in the initial state. We study the one loop processes $e^+e^- \to h^0\gamma$ and $e^-\gamma \to e^- h^0$, we show that it is possible to correlate the total cross section predictions with the couplings $h^0\gamma\gamma$ and $h^0\gamma Z$ which are sensitive to the presence of singly and doubly charged Higgs. For parameter points allowed by the current experimental constraints, our numerical results show that the effect of $H^\pm$ and $H^{\pm\pm}$ can be as large as $\pm$ 25\% with respect to the SM predictions. For both processes, we also present differential cross section for different center of mass energy.