# Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a $W$ pair and to the triple gauge couplings $ZWW$ and $\gamma^*WW$

## TL;DR

This paper calculates two-loop master integrals for QCD corrections to Higgs and gauge boson interactions, providing essential components for precise theoretical predictions in particle physics.

## Contribution

It introduces a canonical basis of master integrals for two-loop corrections involving massive and massless quarks with arbitrary external masses, using the Magnus exponential method.

## Key findings

- Master integrals expressed as a Taylor series in epsilon up to order four.
- Coefficients written in Goncharov polylogarithms up to weight four.
- Results applicable to Higgs decay and gauge boson vertex corrections.

## Abstract

We compute the two-loop master integrals required for the leading QCD corrections to the interaction vertex of a massive neutral boson $X^0$, e.g. $H,Z$ or $\gamma^{*}$, with a pair of $W$ bosons, mediated by a $SU(2)_L$ quark doublet composed of one massive and one massless flavor. All the external legs are allowed to have arbitrary invariant masses. The Magnus exponential is employed to identify a set of master integrals that, around $d=4$ space-time dimensions, obey a canonical system of differential equations. The canonical master integrals are given as a Taylor series in $\epsilon = (4-d)/2$, up to order four, with coefficients written as combination of Goncharov polylogarithms, respectively up to weight four. In the context of the Standard Model, our results are relevant for the mixed EW-QCD corrections to the Higgs decay to a $W$ pair, as well as to the production channels obtained by crossing, and to the triple gauge boson vertices $ZWW$ and $\gamma^*WW$.