Top quark pairs at two loops and Reduze 2

TL;DR

This paper advances the analytical calculation of two-loop corrections for top quark pair production, utilizing Goncharov polylogarithms and introducing Reduze 2's distributed reduction algorithms.

Contribution

It presents new analytical solutions for complex master integrals and introduces Reduze 2's distributed Laporta algorithm and graph matroid methods for automated Feynman integral reduction.

Findings

Analytical solutions for non-planar double box integrals with massive propagators.

Implementation of Reduze 2's distributed reduction algorithms.

Automated calculation of shift relations between Feynman integrals.

Abstract

We report on progress for the analytical calculation of the two-loop corrections to top quark pair production at hadron colliders. For the light fermionic corrections in the gluon channel, we discuss the analytical solution for the master integrals of a non-planar double box with a massive propagator. The result in terms of Goncharov's multiple polylogarithms is handled using systematic reductions based on the symbol map and the coproduct. We discuss new features of the computer program Reduze 2. It provides a fully distributed variant of Laporta's algorithm to reduce loop integrals. New graph matroid based algorithms allow to calculate shift relations between Feynman integrals in a fully automated way.