Treatment of the infrared contribution: NLO QED evolution as a pedagogic example

TL;DR

This paper highlights an inconsistency in the standard NLO DGLAP evolution approach related to infrared contributions, demonstrating a more consistent physical method using QED as an example.

Contribution

It introduces a physical approach that properly handles infrared divergences in NLO QED evolution, improving the theoretical consistency over conventional methods.

Findings

Conventional NLO DGLAP treatment has an IR inconsistency.

A physical method removes IR divergences in QED evolution.

The approach allows calculations in 4-dimensional space without divergences.

Abstract

We show that the conventional prescription used for DGLAP parton evolution at NLO has an inconsistent treatment of the contribution from the infrared (IR) region. We illustrate the problem by studying the simple example of QED evolution, treating the electron and photon as partons. The deficiency is not present in a physical approach which removes the IR divergency and allows calculation in the normal 4-dimensional space.