Renormalization of the gluon distribution function in the background field formalism

TL;DR

This paper derives the leading order DGLAP evolution of the gluon distribution function using the background field formalism in light cone gauge, aiming to unify QCD evolution approaches for collinear and small x physics.

Contribution

It introduces a derivation of gluon distribution evolution in the background field formalism, connecting collinear and small x QCD evolution frameworks.

Findings

Derived LO DGLAP evolution in background field formalism.

Regulated spurious singularities with Mandelstam-Leibbrandt prescription.

Established groundwork for a unified QCD evolution framework.

Abstract

We derive the Leading Order DGLAP evolution of gluon distribution function in the target light cone gauge starting from its standard operator definition. The derivation is performed using the background field formalism also employed in the Color Glass Condensate effective theory of small $x$ QCD. We adopt Mandelstam-Leibbrandt prescription to regulate in an unambiguous way the spurious singularity appearing in the light-cone gauge Feynman propagator. UV divergences are regulated via dimensional regularization. The methods introduced in this paper represent the first steps in the construction of a unified framework for QCD evolution, which could address collinear physics as well as small $x$ physics and gluon saturation.