Processes $\gamma \gamma \rightarrow \phi_i\phi_j$ in Inert Higgs Doublet Models and Two Higgs Doublet Models

In this paper, we present a phenomenological analysis of one-loop induced processes $\gamma \gamma \rightarrow \phi_i\phi_j$, where the CP-even Higgs bosons are denoted as $\phi_{i,j} \equiv h,~H$, in high-energy photon-photon collisions, within the frameworks of the Inert Higgs Doublet Model and the Two Higgs Doublet Model. The total cross sections are evaluated as functions of the center-of-mass energy, finding that the cross sections for the considered processes in all the models under investigation are significantly enhanced around the threshold for charged Higgs boson pair production ($\sim 2 M_{H^\pm}$). Furthermore, the enhancement factors, defined as the ratios of cross sections of $\gamma \gamma \rightarrow \phi_i\phi_j$ in the investigated models to those for $\gamma \gamma \rightarrow hh$ in the Standard Model, are examined in the relevant regions of the model's parameter space. In the Inert Higgs Doublet Model, the factors are studied in the parameter space of $(M_{H^\pm},~\mu^2_2)$ and $(M_{H^\pm},~\lambda_2)$. In the Two Higgs Doublet Model, the factors are examined in the planes defined by $(M_{H^\pm},~t_{\beta})$ as well as in the space of the charged Higgs mass $M_{H^\pm}$ and the soft-breaking $Z_2$ parameter $m_{12}^2$. Two scenarios characterized by $c_{\beta-\alpha} > 0$ and $c_{\beta-\alpha} < 0$ are studied in further detail. The factors exhibit distinct behaviors between these two scenarios. As a result, it is possible to discriminate between them at future colliders. The dependence of the cross section for the process $\gamma \gamma \rightarrow hH$ on $m_{12}^2$ provides a potential probe of the soft $Z_2$-breaking scale in the Two Higgs Doublet Model.