A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes

TL;DR

This paper presents a simple, unintegrated formula that approximates the infrared singular parts of one-loop QCD amplitudes, facilitating numerical calculations by providing a local counter-term for these divergences.

Contribution

It introduces a straightforward unintegrated formula for infrared poles in one-loop QCD amplitudes, enhancing numerical computation methods.

Findings

The formula accurately approximates integrand behavior in soft and collinear regions.

It serves as an effective local counter-term for infrared singularities.

The approach simplifies the numerical evaluation of one-loop QCD amplitudes.

Abstract

We show that a well-known simple formula for the explicit infrared poles of one-loop QCD amplitudes has a corresponding simple counterpart in unintegrated form. The unintegrated formula approximates the integrand of one-loop QCD amplitudes in all soft and collinear singular regions. It thus defines a local counter-term for the infrared singularities and can be used as an ingredient for the numerical calculation of one-loop amplitudes.