# Two-loop master integrals for the mixed QCD-electroweak corrections for $H \rightarrow b\bar{b}$ through a $H t \bar{t}$-coupling

## TL;DR

This paper computes two-loop master integrals for mixed QCD-electroweak corrections to the Higgs decay into bottom quarks via a top-quark loop, incorporating full heavy mass dependence and expressing results with polylogarithms.

## Contribution

It provides the first complete calculation of two-loop integrals for this specific Higgs decay process with full mass dependence.

## Key findings

- Explicit expressions for master integrals in terms of polylogarithms.
- Rationalization of square roots in the integrals.
- Facilitates precise theoretical predictions for Higgs decay rates.

## Abstract

We present the two-loop master integrals relevant to the ${\mathcal O}(\alpha \alpha_s)$-corrections to the decay $H \rightarrow b \bar{b}$ through a $H t \bar{t}$-coupling. We keep the full dependence on the heavy particle masses, but neglect the $b$-quark mass. The occurring square roots can be rationalised and the result is expressed in terms of multiple polylogarithms.