A complete reduction of one-loop tensor 5- and 6-point integrals

TL;DR

This paper presents a comprehensive analytical reduction method for one-loop Feynman integrals with five and six external legs, enabling efficient computation and analysis of tensor integrals up to certain ranks.

Contribution

It introduces an elegant formalism using signed minors for reducing high-point tensor integrals, avoiding inverse Gram determinants, and provides compact formulas suitable for numerical implementation.

Findings

Reduced 6-point tensor functions to 5-point functions

Expressed tensor functions in terms of scalar integrals

Implemented in Fortran and Mathematica for practical use

Abstract

We perform a complete analytical reduction of general one-loop Feynman integrals with five and six external legs for tensors up to rank R=3 and 4, respectively. An elegant formalism with extensive use of signed minors is developed for the cancellation of inverse Gram determinants. The 6-point tensor functions of rank R are expressed in terms of 5-point tensor functions of rank R-1, and the latter are reduced to scalar four-, three-, and two-point functions. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. They are implemented in Fortran and Mathematica.