Higgs photon associated production in a Two Higgs Doublet Type-II Seesaw Model at future electron-positron colliders

We study the one-loop prediction for the single production of a SM-like Higgs boson in association with a photon in electron-positron collisions in the context of the two Higgs doublet type-II seesaw model ($2HDMcT$). We explore to what extent the new scalars in the $2HDMcT$ spectrum affect its production cross-section, the ratio $R_{\gamma h_1}$ as well as the signal strengths $R_{\gamma Z}$ and $R_{\gamma \gamma}$ when $h_1$ is identified with the observed $SM$ Higgs boson within the $2HDMcT$ delimited parameter space. More specifically, we focus on $e^+e^- \to h_1\gamma$ process at one-loop, and analyzed how it evolves under a full set of theoretical constraints and the available experimental data, including $B\to X_s\gamma$ limit at 95$\%$ C.L. Our analysis shows that these observables are strongly dependent on the parameters of the model, especially the mixing angel $\alpha_1$, the potential parameters $\lambda_{7}$, $\lambda_{9}$, the trilinear Higgs couplings, with a noticeable sensitivity to $\alpha_1$. We found that $\sigma (e^+e^- \to h_1\gamma)$ can significantly be enhanced up to $8.1\,\,\times 10^{-2}$ fb, thus exceeding the Standard Model prediction. Additionally, as a byproduct, we also observed that $R_{\gamma h_1}$ is entirely correlated with both the $h_1\to\gamma\gamma$ and $h_1\to\gamma Z$ signal strengths.