On the tensor reduction of one-loop pentagons and hexagons

TL;DR

This paper develops analytical methods for reducing complex one-loop tensor integrals with five and six external legs into simpler scalar master integrals, using recurrence relations and signed minors, with implementation in a Mathematica package.

Contribution

It introduces a new compact reduction technique for one-loop pentagon and hexagon tensor integrals using recurrence relations and signed minors, implemented in a Mathematica package.

Findings

Reductions expressed in terms of signed minors.

Implementation of reduction algorithms in hexagon.m.

Numerical examples demonstrating the method's effectiveness.

Abstract

We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are expressed in a compact form in terms of signed minors, and have been implemented in a mathematica package called hexagon.m. We present several numerical examples.