Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel

TL;DR

This paper provides a comprehensive analytic calculation of two-loop QCD helicity amplitudes for top quark pair production via gluon fusion, including novel massive fermion loop corrections involving elliptic integrals.

Contribution

It introduces the first complete analytic expressions for these amplitudes with massive fermion loops and elliptic integrals, advancing precision in top quark production calculations.

Findings

Analytic expressions for two-loop helicity amplitudes including massive loops

Complete set of master integrals with elliptic curve integrals

Numerical evaluation methods for complex iterated integrals

Abstract

We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.