Feynman integral reduction by covariant differentiation

TL;DR

The paper introduces an efficient method for reducing Feynman integrals to master integrals using covariant differentiation, implemented in the MERLIN Mathematica code.

Contribution

It presents a novel covariant differentiation approach for Feynman integral reduction, applicable across various configurations with a one-time topology setup.

Findings

Reduces Feynman integrals to master integrals efficiently.

Implementation available in the MERLIN Mathematica package.

Applicable to different internal propagator mass configurations.

Abstract

We show how a large class of Feynman integrals can be efficiently reduced to master integrals by suitable covariant differentiation on the vector space dual to the one spanned by the master integrals. The connections needed in the covariant derivatives have to be built only once for a given topology and then apply to any configuration of internal propagator masses. We implement our algorithm in the Mathematica code Method for Reduction of Loop Integrals (MERLIN).