Symbolic syzygy-constrained reduction rules for Feynman integrals and the LoopIn framework

TL;DR

This paper introduces a novel algorithm for efficient IBP reduction of complex Feynman integrals, avoiding large intermediate systems, and presents LoopIn, a framework for automating multi-loop calculations.

Contribution

The paper presents a new reduction algorithm that simplifies IBP calculations and integrates it into the LoopIn framework for automated multi-loop computations.

Findings

Successfully applied to high-rank integrals in complex topologies

Achieved faster IBP reduction in black hole binary scattering amplitudes

Demonstrated efficiency with non-trivial multi-loop examples

Abstract

We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us to avoid a large intermediate system of equations and instead focus on applying direct reduction rules to the integrals. We demonstrate the application of our algorithm with some highly non-trivial examples, namely rank-20 integrals for the double box with an external mass and the massless pentabox. We also achieve much faster IBP reduction for an example of scattering amplitudes for spinning black hole binary systems. Finally, we present LoopIn, a modular framework for automating multi-loop calculations, where the IBP techniques described here can be interfaced.