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

TL;DR

This paper calculates the one-loop contributions of W bosons to the decay process H→Zγ within the general R_ξ gauge, confirming gauge independence and providing analytical results compatible with previous findings.

Contribution

It provides explicit analytical expressions for W boson contributions in the R_ξ gauge, demonstrating gauge parameter independence and numerical stability across different ξ values.

Findings

Analytical results expressed with Passarino-Veltman functions.

Gauge independence confirmed both analytically and numerically.

Results stable for various ξ values, including 0, 1, 100, and infinity.

Abstract

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 which their numerical evaluations can be generated using {\tt 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 are also checked numerically for consistence. Our results are also well stable with different values of $\xi =0, 1, 100,$ and $\xi \rightarrow \infty$.