The one loop gluon emission light cone wave function

TL;DR

This paper calculates the one-loop gluon emission light cone wave function using light cone perturbation theory in a helicity basis, addressing divergence regularization and renormalization in QCD.

Contribution

It provides the first explicit one-loop calculation of the gluon emission wave function in a helicity basis within light cone perturbation theory.

Findings

Ultraviolet divergences are absorbed into the QCD running coupling.

Explicit finite part of the wave function is derived after renormalization.

Method demonstrates how to handle divergences in light cone calculations.

Abstract

Light cone perturbation theory has become an essential tool to calculate cross sections for various small-$x$ dilute-dense processes such as deep inelastic scattering and forward proton-proton and proton-nucleus collisions. Here we set out to do one loop calculations in an explicit helicity basis in the four dimensional helicity scheme. As a first process we calculate light cone wave function for one gluon emission to one-loop order in Hamiltonian perturbation theory on the light front. We regulate ultraviolet divergences with transverse dimensional regularization and soft divergences with using a cut-off on longitudinal momentum. We show that when all the renormalization constants are combined, the ultraviolet divergences can be absorbed into the standard QCD running coupling constant, and give an explicit expression for the remaining finite part.