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.

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 $\gamma^*WW$.