Master integrals for ${\cal O}(\alpha \alpha_s)$ corrections to $H \to ZZ^*$

TL;DR

This paper provides analytic solutions for master integrals needed for two-loop electroweak and QCD corrections to Higgs decay into Z bosons, using differential equations and rationalization techniques for multiple mass scales.

Contribution

It introduces a method to solve complex master integrals with multiple mass scales by rationalizing three square roots and constructing dlog-forms, advancing precision calculations in Higgs physics.

Findings

Analytic expressions for all relevant master integrals are obtained.

The differential equations are solved using Chen's iterated integrals with dlog forms.

The approach handles multiple mass scales and square roots effectively.

Abstract

We present analytic results for all the Feynman integrals relevant for ${\mathcal O}(\alpha \alpha_s)$ virtual corrections to $H \rightarrow ZZ^*$ decay. We use the method of differential equations to solve the master integrals while keeping the full dependence on the masses of all the particles including internal propagators. Due to the presence of four mass scales we encounter multiple square roots. We argue that all the occurring square roots can not be rationalized at the same time as a simultaneous rationalization brings us to integrals over $CY_3$ manifolds. Hence we rationalize only three square roots simultaneously and construct suitable ans\"atze to obtain dlog-forms containing the square root, after obtaining an epsilon-factorised form for the differential equations. We present the alphabet and the analytic form of all the boundary constants that appear in the solutions of the differential equations. The results for master integrals are expressed in terms of Chen's iterated integrals with dlog one-forms.