Rapidity divergences and valid definitions of parton densities

TL;DR

The paper discusses the issue of rapidity divergences in defining parton densities in gauge theories, proposing modifications to remove these divergences for better phenomenological and non-perturbative applications.

Contribution

It reviews the nature of rapidity divergences and introduces modified definitions of parton densities to eliminate these divergences, impacting both phenomenology and light-front quantization.

Findings

Modified definitions remove rapidity divergences.

Essential for accurate QCD phenomenology.

Affects formulation of light-front quantization.

Abstract

Rapidity divergences occur when parton densities in a gauge theory are defined in the most natural way, as expectation values of partonic number operators in light-front quantization. I review these and other related divergences, and show how the definitions of parton densities can be modified to remove the divergences. A modified definition is not only essential for many phenomenological applications of QCD, but also concerns the treatment of parton densities in non-perturbative approaches. The necessity of modifications in the definition of a parton density also entails corrections in the formulation of light-front quantization for gauge theories.