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

By Xiao Liu, Yan-Qing Ma, Chen-Yu Wang. 2017

229 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c6c22d26c20e46b1b3f5edf3f26e373b5f74e905

Citations in the corpus

• Integral reduction with Kira 2.0 and finite field methods (2020, unknown): “In the last few years, new techniques have been explored and applied to integral reduction problems, employing syzygy equations [7–12], algebraic geometry [13–15], intersection numbers [16–20], finite field and interpolation techniques [21–26], or special integral representations [27–30].”