Reduction Method for One-loop Tensor 5- and 6-point Integrals Revisited

TL;DR

This paper reviews a comprehensive analytical reduction method for one-loop tensor integrals with five and six external legs, enabling efficient computation and analysis of these complex Feynman integrals.

Contribution

It introduces a formalism using signed minors that simplifies the reduction process and cancels leading inverse Gram determinants, improving analytical and numerical handling.

Findings

Developed compact formulas for tensor integrals with five and six legs.

Demonstrated the cancellation of leading inverse Gram determinants.

Provided numerical examples illustrating the method's effectiveness.

Abstract

A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants.The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented.