Master integrals contributing to two-loop leading colour QCD helicity amplitudes for top-quark pair production in the gluon fusion channel

TL;DR

This paper computes master integrals necessary for two-loop QCD helicity amplitudes in top-quark pair production via gluon fusion, including complex elliptic integrals and singularity structures.

Contribution

It provides the complete set of master integrals for two-loop leading-colour amplitudes, incorporating massive fermion loop corrections and elliptic curve integrals.

Findings

Derived master integrals involving elliptic curves.

Analyzed singularity structures for numerical evaluation.

Enhanced understanding of analytic continuation in amplitude calculations.

Abstract

We present the master integrals relevant for computing the complete set of leading-colour analytic helicity amplitudes for top-quark pair production via gluon fusion at two-loops in QCD. We include corrections due to massive fermion loops which give rise to integrals involving elliptic curves. We also elaborate on the structure of singularities that play an important role in the numerical evaluation of the iterated integrals and their analytic continuation.