One-loop $W$ boson contributions to the decay $H\rightarrow Z\gamma$ in the general $R_\xi$ gauge

One-loop $W$ boson contributions to the decay $H\rightarrow Z\gamma$ in the general $R_\xi$ gauge are presented. The analytical results are expressed in terms of well-known Passarino–Veltman functions such that their numerical evaluations can be generated using $\texttt{LoopTools}$. In the limit $d\rightarrow 4$, we have shown that these analytical results are independent of the unphysical parameter $\xi$ and consistent with previous results. The gauge parameter independence is also checked numerically for consistence. Our results are also well stable with different values of $\xi =0,\ 1,\ 100$ and $\xi \rightarrow \infty$.