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

Abstract

We present the first rainbow-ladder Dyson-Schwinger equations study of the pion's chiral-odd, twist-3 parton distribution $e_{\mathrm{q}}(x)$. 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 $f_{\mathrm{q}}(x)$ and the twist-3 distribution $e_{\mathrm{q}}(x)$. Our results show that chiral symmetry strongly suppresses the twist-2 component of $e_{\mathrm{q}}(x)$, 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.

6 pages, 2 figures