One-loop form factors for $H\rightarrow \gamma^*\gamma^*$ in $R_{\xi}$ gauge

In this paper, we present general one-loop form factors for $H\rightarrow \gamma^* \gamma^*$ in $R_{\xi}$ gauge, considering all cases of two on-shell, one on-shell and two off-shell for final photons. The calculations are performed in standard model and in arbitrary beyond the standard models which charged scalar particles may be exchanged in one-loop diagrams. Analytic results for the form factors are shown in general forms which are expressed in terms of the Passarino-Veltman functions. We also confirm the results in previous computations which are available for the case of two on-shell photons. The $\xi$-independent of the result is also discussed. We find that numerical results are good stability with varying $\xi=0,1$ and $\xi\rightarrow \infty$.