A Note on the IR Finiteness of Fermion Loop Diagrams

TL;DR

This paper proves that the most general fermion loop diagrams are IR finite in all regions and relates their IR singularities to those of simpler scalar integrals, advancing understanding of quantum field theory calculations.

Contribution

It establishes the IR finiteness of general fermion loop diagrams and connects their IR structure to that of reduced scalar integrals, providing new insights into loop diagram analysis.

Findings

Fermion loop diagrams are IR finite in soft and collinear regions.

IR singular structure of box scalar integrals can be expressed via reduced triangle integrals.

The result simplifies the analysis of IR divergences in quantum field theory.

Abstract

We show that the most general fermion loop diagram is finite in both soft and collinear regions and therefore, it's IR finite. We use this result to express the IR singular structure of a box scalar integral in terms of the IR singular structure of reduced triangle scalar integrals.