A Systematic and Efficient Method to Compute Multi-loop Master Integrals

TL;DR

This paper introduces a new systematic numerical method for computing multi-loop master integrals using differential equations, offering high precision and faster performance than existing methods, and also proposes a novel approach for scalar one-loop integrals.

Contribution

The paper presents a novel numerical approach for multi-loop master integrals based on differential equations with simple boundary conditions, improving efficiency and general applicability.

Findings

Achieves high-precision results for multi-loop integrals.

Significantly faster than sector decomposition methods.

Introduces a new strategy for scalar one-loop integrals.

Abstract

We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals.