Mixed QCD-EW corrections for Higgs leptonic decay via $HW^+W^-$ vertex

TL;DR

This paper computes two-loop mixed QCD-electroweak corrections to the $HW^+W^-$ vertex, providing analytic formulas for decay and production processes involving the Higgs and W bosons, enhancing precision in theoretical predictions.

Contribution

It introduces a method to analytically evaluate two-loop integrals for the $HW^+W^-$ vertex using Baikov representation and intersection theory, enabling precise calculations of Higgs decay and production.

Findings

Analytic expressions for master integrals in terms of multiple polylogarithms.

Application of results to Higgs decay $H o u_e e W$ with detailed decay rate analysis.

Potential use in Higgs production via W boson fusion.

Abstract

We consider the two-loop corrections to the $HW^+W^-$ vertex at order $\alpha\alpha_s$. We construct a canonical basis for the two-loop integrals using the Baikov representation and the intersection theory. By solving the $\epsilon$-form differential equations, we obtain fully analytic expressions for the master integrals in terms of multiple polylogarithms, which allow fast and accurate numeric evaluation for arbitrary configurations of external momenta. We apply our analytic results to the decay process $H \to \nu_e e W$, and study both the integrated and differential decay rates. Our results can also be applied to the Higgs production process via $W$ boson fusion.