Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight

TL;DR

This paper introduces a new protocol using Baikov representation to identify Feynman integrals with uniform transcendental weight, leveraging recent mathematical advances for complex multi-scale diagrams.

Contribution

It presents a novel leading singularity analysis method in Baikov representation for finding UT integrals, especially in multi-scale Feynman diagrams.

Findings

Successfully determined the UT basis for a two-loop diagram with three mass scales.

Utilized rationalization of square roots and syzygy computations in the approach.

Demonstrated effectiveness in complex multi-scale Feynman integral analysis.

Abstract

We provide a leading singularity analysis protocol in Baikov representation, for the searching of Feynman integrals with uniform transcendental (UT) weight. This approach is powered by the recent developments in rationalizing square roots and syzygy computations, and is particularly suitable for finding UT integrals with multiple mass scales. We demonstrate the power of our approach by determining the UT basis for a two-loop diagram with three external mass scales.