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  • Letter
  • Open Access

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

Chao Shi1,*, Liming Lu1, Ian C. Cloët2,†, Wenbao Jia1, and Peter C. Tandy3,‡

  • *Contact author: cshi@nuaa.edu.cn
  • †Contact author: icloet@anl.gov
  • ‡Contact author: tandy@kent.edu
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Phys. Rev. D 113, L111501 – Published 3 June, 2026

DOI: https://doi.org/10.1103/yklv-ntq9

Abstract

We present the first rainbow-ladder Dyson-Schwinger equations study of the pion’s chiral-odd, twist-3 parton distribution eq(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 fq(x) and the twist-3 distribution eq(x). Our results show that chiral symmetry strongly suppresses the twist-2 component of eq(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.

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Phys. Rev. D 113, L111501– Published 3 June, 2026
  • Received 26 February 2026
  • Accepted 4 May 2026
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