Parton distribution function for the gluon condensate

TL;DR

This paper introduces a twist-four parton distribution function related to the gluon condensate in the nucleon, exploring its theoretical properties and performing one-loop calculations for different targets.

Contribution

It proposes a new distribution function linked to the gluon condensate and analyzes its theoretical features and one-loop behavior for quark and gluon targets.

Findings

First moment equals the gluon condensate

Equation of motion relations derived

Possible delta function contribution at zero momentum fraction

Abstract

Motivated by the desire to understand the nucleon mass structure in terms of light-cone distributions, we introduce the twist-four parton distribution function $F(x)$ whose first moment is the gluon condensate in the nucleon. We present the equation of motion relations for $F(x)$ and discuss the possible existence of the delta function (`zero mode') contribution at $x=0$. We also perform one-loop calculations for quark and gluon targets.