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 $e_{\rm q}(x)$. 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.

Figures (2)

• Figure 1: The first three rows are the rainbow--ladder truncated DSEs for dressed quark propagator $S$, the amputated Bethe-Salpeter bound state vertex $\Gamma_{\chi}(k;P)$, and the amputated quark-quark correlation matrix $\Gamma_\Phi(k;P)$ respectively. The fourth row relates the unamputated quark-quark correlation matrix $\Phi(k;P)$ to $\Gamma_\Phi(k;P)$.
• Figure 2: Upper Panel: The pion PDFs at model scale $\mu_0=0.63$ GeV. Lower Panel: The pion PDFs $f_{\rm q}(x)$ and $e_{\rm q}(x)$ at $\mu =1.3$ GeV with $f_{\rm q}(x)$ compared to the JAM analysis at NLO Barry:2018ort. Also shown for comparison are isospin averaged proton PDF data: the $e_{\rm q}(x)$ CLAS data points at approximately $1$ GeV Courtoy:2022kca, and the MSHT fit of the proton $f_{\rm q}(x)$Bailey:2020ooq.