Feynman Integral Reduction and Landau Singularities

TL;DR

This paper introduces a new approach to Feynman integral reduction based on Landau equations and syzygy methods, offering a more efficient and physically insightful way to handle complex integrals in particle physics.

Contribution

It develops a determinantal method linking Landau singularities with syzygy solutions, advancing the computational techniques for Feynman integral reduction.

Findings

Demonstrates the method on two-loop five-point integrals for top quark production.

Provides compact, transparent solutions for integral reduction.

Suggests an efficient new approach with physical insights into Feynman integrals.

Abstract

We propose that Feynman integral reduction is controlled by solutions of the Landau equations. We study integral relations with prescribed propagator powers using syzygy methods and discuss how syzygies can be expressed as a sum over components of the Landau singularity locus. This leads to a determinantal approach to solving the syzygy problem, giving rise to highly compact and physically transparent solutions. We demonstrate the method in applications to planar two-loop five-point integrals relevant for the $pp \rightarrow t\overline{t}H$ process. Our results suggest an efficient method of Feynman integral reduction and provide a novel physical perspective on the problem.