IR finite one-loop box scalar integral with massless internal lines

TL;DR

The paper tackles the IR finite one-loop box scalar integral with massless internal lines, a key ingredient in NLO pQCD calculations. It employs Mellin–Barnes representations to relate the box integral to the IR finite triangle integral plus a correction term, yielding a compact result expressed with only two dilogarithms and simple logarithms. The authors provide a general, sign-aware formulation that is valid across all kinematic regions and facilitates separating real and imaginary parts for numerical work, with numerical agreement to prior results (e.g., Denner) across the phase space. This approach streamlines the evaluation of one-loop box integrals and enhances numerical stability in practical computations.

Abstract

The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments.

Figures (2)

• Figure 1: One-loop box diagram.
• Figure 2: One-loop triangle diagram.