J_AW,WA functions in Passarino-Veltman reduction

TL;DR

This paper analyzes a special class of Passarino-Veltman functions J, used in infrared divergent box diagram reductions, providing a method to separate singularities and express functions in terms of regularized, explicit combinations.

Contribution

It introduces a procedure to separate infrared and mass singularities in Passarino-Veltman functions J, expressing them as regular, explicit combinations of standard functions, with extensive numerical validation.

Findings

Functions J are expressed as linear combinations of D0 and C0 functions.

Singularities are separated and absorbed into simple C0 functions.

Numerical results agree with LoopTools calculations.

Abstract

In this paper we continue to study a special class of Passarino-Veltman functions J arising at the reduction of infrared divergent box diagrams. We describe a procedure of separation of two types of singularities, infrared and mass singularities, which are absorbed in simple C0 functions. The infrared divergences of C0's can be regularized then by any method: photon mass, dimensionally or by the width of an unstable particle. Functions J, in turn, are represented as certain linear combinations of the standard D0 and C0 Passarino-Veltman functions. The former are free of both types of singularities and are expressed as explicit and compact linear combinations of logarithms and dilogarithm functions. We present extensive comparisons of numerical results with those obtained with the aid of the LoopTools package.