$J$ functions for the process ud$\to$WA

TL;DR

This paper introduces a universal analytic approach for calculating specific $J$ functions arising in infrared-divergent box diagrams of the process $ud\to WA$, providing explicit formulas and numerical validation.

Contribution

It presents a systematic method to express $J$ functions as finite, singularity-free combinations of standard $D_0$ and $C_0$ functions, improving analytic calculations.

Findings

Derived explicit formulas for $J$ functions in terms of dilogarithms.

Validated the approach with numerical comparisons to LoopTools.

Provided a systematic way to handle infrared divergences in box diagrams.

Abstract

In this paper we present a description of the universal approach for analytic calculations for a certain class of $J$ functions for six topologies of the boxes for process $ud\rightarrow WA$. These functions $J$ arise at the reduction of infrared divergent box diagrams. The standard Passarino--Veltman reduction of four-point box diagram with an internal photon line connecting two external lines on the mass shell leads to infrared-divergent and mass-singular $D_0$ functions. In the system SANC a systematic procedure is adopted to separate both types of singularities into the simplest objects, namely $C_0$ functions. The functions $J$, in turn, are represented as certain linear combinations of the standard $D_0$ and $C_0$ functions. The subtracted $J$ functions are free of both types of singularities and are expressed as explicit and compact linear combinations of dilogarithm functions. We present extensive comparisons of numerical results of SANC with those obtained with the aid of the LoopTools package.