Infrared scalar one-loop three point integrals in loop regularization

TL;DR

This paper evaluates infrared divergent scalar three-point integrals using loop regularization, providing analytic results and a method to regulate divergences with a sliding scale, enhancing understanding of infrared behavior in quantum field theory.

Contribution

It introduces a systematic loop regularization approach for infrared divergent three-point integrals, including massless and massive cases, with analytic expressions and a scale-dependent regulation method.

Findings

Analytic expressions for infrared divergent triangle integrals.

A regulation scheme using a sliding scale $_s$.

Insights into the scale dependence of amplitudes.

Abstract

The infrared divergent scalar three-point integrals are evaluated by the loop regularization method. Three kinds of infrared divergent integrals, i.e., massless triangle diagram, triangle diagrams with one and two massive internal lines, are systematically evaluated by loop regularization, analytic results are obtained. According the method, the infrared divergences are regulated by the so-called sliding scale $\mu_{s}$ which plays the role of infrared cutoff. The amplitudes obtained through loop regularization depend on $\mu_{s}$ such that we may extract different contribution by varying $\mu_{s}$. Some general results for evaluation of scale one-loop triangle diagram are also derived.