Breaking the 2-loop barrier for generalized IBP reduction

TL;DR

This paper presents an optimized method for constructing differential operators in generalized IBP reduction at the 2-loop level, significantly improving efficiency by using partial operators that target individual polynomials.

Contribution

It introduces a novel approach using partial operators to simplify the construction of differential operators in 2-loop IBP reduction, enabling more efficient computations.

Findings

Optimized software efficiently constructs differential operators for 2-loop IBP reduction.

Partial operators are more effective than complete ones for this task.

The method advances the computational feasibility of complex Feynman integral reductions.

Abstract

We discuss the problem of constructing differential operators for the generalized IBP reduction algorithms at the 2-loop level. A deeply optimized software allows one to efficiently construct such operators for the first non-degenerate 2-loop cases. The most efficient approach is found to be via the so-called partial operators that are much simpler than the complete ones, and that affect the power of only one of the polynomials in the product.