One-loop Feynman Integral Reduction by Differential Operators

TL;DR

This paper introduces an improved differential operator method for one-loop Feynman integral reduction, providing explicit algebraic recurrence relations for reduction coefficients, enhancing the efficiency over traditional methods.

Contribution

The paper develops a complete integral reduction technique for one-loop integrals using differential operators, extending previous tadpole reduction results.

Findings

Analytic expressions for reduction coefficients are obtained via algebraic recurrence relations.

The method is demonstrated with explicit examples showing its effectiveness.

It offers an improved alternative to the Passarino-Veltman reduction.

Abstract

For loop integrals, the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman reduction. Inspired by the recent paper [1] where the tadpole reduction coefficients have been solved, in this paper we show the same technique can be used to give a complete integral reduction for any one-loop integrals. The differential operator method is an improved version of the PV-reduction method. Using this method, analytic expressions of all reduction coefficients of the master integrals can be given by algebraic recurrence relation easily. We demonstrate our method explicitly with several examples.