J _AW,WA functions in Passarino-Veltman reduction

Abstract

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 C ₀ functions. The infrared divergences of C ₀’s can be regularized then by any method: photon mass, dimensionally or by the width of an unstable particle. Functions D ₀ are represented as certain linear combinations of the standard C ₀ Passarino-Veltman functions and infrared finite functions J. Then mass singularities are extracted from J to other combinations of C ₀. The rests are free of both types of singularities and are expressed as explicit and compact linear combination of logarithms and dilogarithm functions. The extensive comparison of numerical results with those obtained with the aid of the Loop Tools package is presented.