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 $\xi \rightarrow \infty$.

中文翻译：

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单环 $W$ 玻色子对一般 $R_\xi$ 规范中衰变 $H\rightarrow Z\gamma$ 的贡献

给出了一般 $R_\xi$ 规范中对衰变 $H\rightarrow Z\gamma$ 的单环 $W$ 玻色子贡献。分析结果用著名的 Passarino-Veltman 函数表示，因此可以使用 $\texttt{LoopTools}$ 生成它们的数值评估。在极限$d\rightarrow 4$，我们已经证明这些分析结果独立于非物理参数$\xi$，并且与之前的结果一致。规范参数独立性也通过数字检查一致性。我们的结果在 $\xi =0,\1,\100$ 和 $\xi\rightarrow\infty$ 的不同值下也很稳定。