Parton Distributions of Gluons in Different Representations

TL;DR

This paper proves that gluon distributions in fundamental and adjoint representations are identical when gauge links are uniformly future- or past-pointing, clarifying the axial gauge puzzle in quantum chromodynamics.

Contribution

It provides a proof that gluon distributions in different $SU(N)$ representations are equivalent under specific gauge link conditions, addressing a key question in gauge invariance.

Findings

Gluon distributions in fundamental and adjoint representations are the same with uniform gauge links.

The axial gauge puzzle arises when gauge links include both future- and past-pointing links.

One-loop analysis shows the conditions under which the distributions differ or agree.

Abstract

It has been questioned if gluon distributions defined in different representations of $SU(N)$ are the same. The question has arisen in the connection to the recently proposed resolution of the so-called axial gauge puzzle. We give a proof that gluon distributions defined in the fundamental- and adjoint representation, where gauge links consist of those which are all future-pointing or all past-pointing, are same. These gauge links are needed to make the distributions gauge invariant. When these links consist of not only future-pointing gauge links but also past-pointing ones, then the puzzle appears. We examine the puzzle for distributions at one-loop in the cases with gauge links along time-like-, space-like- and light-cone direction.