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Top quark pairs at two loops and Reduze 2

Andreas von Manteuffel, Cedric Studerus

TL;DR

The paper addresses analytic two-loop corrections to top quark pair production at hadron colliders, focusing on the light-fermion contributions in the gluon channel. It combines differential equations for master integrals, Mellin-Barnes representations, and Goncharov polylogarithms to obtain analytic results and uses symbol map and coproduct to simplify expressions. It also introduces Reduze 2, a distributed reduction tool with graph- and matroid-based shift-relations that automate reductions across integral families. The work advances NNLO predictions by providing explicit master integrals for a challenging non-planar topology and demonstrates significant simplifications of multi-scale amplitudes, with broad applicability to other processes.

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.

Top quark pairs at two loops and Reduze 2

TL;DR

The paper addresses analytic two-loop corrections to top quark pair production at hadron colliders, focusing on the light-fermion contributions in the gluon channel. It combines differential equations for master integrals, Mellin-Barnes representations, and Goncharov polylogarithms to obtain analytic results and uses symbol map and coproduct to simplify expressions. It also introduces Reduze 2, a distributed reduction tool with graph- and matroid-based shift-relations that automate reductions across integral families. The work advances NNLO predictions by providing explicit master integrals for a challenging non-planar topology and demonstrates significant simplifications of multi-scale amplitudes, with broad applicability to other processes.

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.

Paper Structure

This paper contains 4 sections, 2 figures.

Table of Contents

  1. Top quark pair production at NNLO
  2. Light fermionic two--loop corrections to $gg\to t\bar{t}$
  3. Reduze 2
  4. Conclusion

Figures (2)

  • Figure 1: nameref-fig:npbox fith LAB: fig:npbox A non--planar double box diagram with a massive propagator (thick line) contributing to the light fermionic corrections to top quark pair production in the gluon channel.
  • Figure 2: nameref-fig:matroids fith LAB: fig:matroids Two vacuum graphs which are not isomorphic but have equivalent scalar propagators nevertheless. The graphs are related by a twist and their matroids are isomorphic.