An imprint of intrinsic quark--gluon correlations: a nonmonotonic feature in $e(x)$

TL;DR

This study uses Dyson-Schwinger equations to analyze the pion's twist-3 parton distribution, revealing a nonmonotonic feature caused by intrinsic quark-gluon correlations, which may significantly influence hadronic structure functions.

Contribution

It introduces a novel Dyson-Schwinger equation approach to simultaneously extract twist-2 and twist-3 distributions, highlighting the dominance of genuine twist-3 components with a nonmonotonic structure.

Findings

Genuine twist-3 component features a node and nonmonotonic behavior.

Chiral symmetry suppresses the twist-2 part of $e_q(x)$.

Nonmonotonic structure may impact interpretations of experimental data.

Abstract

We present the first rainbow-ladder Dyson-Schwinger equations study of the pion's chiral-odd, twist-3 parton distribution $e_{\rm q}(x)$. By deriving a novel Dyson-Schwinger equation for the pion's quark-quark correlation matrix, we simultaneously extract from it both the unpolarized twist-2 parton distribution function $f_{\rm q}(x)$ and the twist-3 distribution $e_{\rm q}(x)$. Our results show that chiral symmetry strongly suppresses the twist-2 component of $e_{\rm q}(x)$, leaving the genuine twist-3 quark-gluon component dominant and featuring a node. We therefore argue that the genuine twist-3 term can make a substantial contribution to hadronic $e(x)$, producing a nonmonotonic structure that is a clear imprint of intrinsic quark-gluon correlations. We point out that the existence of a hump-like feature is compatible with, although not uniquely indicated by, recent proton extractions and awaits more precise determination.