# Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel

## TL;DR

This paper analytically computes master integrals for two-loop non-planar QCD corrections in top-quark pair production, advancing precision calculations in particle physics.

## Contribution

It provides the first analytic solutions for these complex integrals using differential equations and harmonic polylogarithms, enhancing theoretical predictions.

## Key findings

- Explicit epsilon expansions of integrals up to weight four
- Use of generalized harmonic polylogarithms for solutions
- Facilitation of precise top-quark pair production calculations

## Abstract

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator $\epsilon$ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four.