Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections

TL;DR

This paper introduces a novel module-intersection IBP method leveraging algebraic geometry to efficiently reduce complex multi-loop Feynman integrals, demonstrated on two-loop five-point non-planar hexagon-box integrals.

Contribution

The paper develops a new IBP reduction technique using module intersections and algebraic geometry, enabling complete analytic reduction of complex non-planar integrals.

Findings

Successfully reduced two-loop five-point non-planar hexagon-box integrals.

Achieved a basis of 73 master integrals.

Demonstrated efficiency of the method on complex multi-scale integrals.

Abstract

We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by explicitly carrying out the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to a basis of $73$ master integrals.