Imprint of intrinsic quark-gluon correlations: A nonmonotonic feature in e ( x )

We present the first rainbow-ladder Dyson-Schwinger equations study of the pion’s chiral-odd, twist-3 parton distribution e 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 q ( x ) and the twist-3 distribution e q ( x ) . Our results show that chiral symmetry strongly suppresses the twist-2 component of e 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 humplike feature is compatible with, although not uniquely indicated by, recent proton extractions and awaits more precise determination.