Associated Production of Higgs at Linear Collider in the Inert Higgs Doublet Model

We study the correlation between the Standard Model Higgs decay $h\to \gamma \gamma$ and $h\to Z \gamma$ in the Inert Higgs Doublet Model. It is found that these two one-loop-induced decays are positively correlated, with the later channel having slightly smaller branching ratio than the former one. At the Linear Collider, we study the interplay of the off-shell extension of these two amplitudes that contributed significantly to the associated production of the Higgs boson with a photon in the process $e^+ e^- \to \gamma h$ and with an electron in the process $e^-\gamma \to e^- h$ in the $s$ and $t$ channels respectively via both $\gamma$ and $Z$ exchange for each process.