The Gluon Distribution Function and Factorization in Feynman Gauge

TL;DR

This paper investigates the complexities of factorization in Feynman gauge, revealing how non-cancellation of super-leading terms from longitudinal gluons, due to their transverse momenta and non-Abelian gauge properties, is essential for defining gauge-invariant gluon distributions.

Contribution

It demonstrates that residual leading terms from longitudinal gluons persist in Feynman gauge, clarifying their role in the gauge-invariant formulation of gluon distribution functions.

Findings

Super-leading terms cancel after summing graphs.

Residual leading terms from longitudinal gluons remain due to transverse momenta.

Non-Abelian gauge properties are crucial for correct gluon distribution functions.

Abstract

A complication in proving factorization theorems in Feynman gauge is that individual graphs give a super-leading power of the hard scale when all the gluons inducing the hard scattering are longitudinally polarized. With the aid of an example in gluon-mediated deep inelastic scattering, we show that, although the super-leading terms cancel after a sum over graphs, there is a residual non-zero leading term from longitudinally polarized gluons. This is due to the non-zero transverse momenta of the gluons in the target. The non-cancellation, due to the non-Abelian property of the gauge group, is necessary to obtain the correct form of the gluon distribution function as a gauge-invariant matrix element.