DSE inspired model for the pion's valence dressed-quark GPD

TL;DR

This paper develops a Dyson-Schwinger equation-based approach to compute the pion's valence dressed-quark GPD, correcting previous impulse approximation methods and providing a more accurate picture of the pion's internal structure.

Contribution

It introduces a correction to the impulse approximation for the pion's GPD using a Dyson-Schwinger equation framework, improving the understanding of pion structure at a hadronic scale.

Findings

Corrected the impulse approximation for the pion's GPD.

Provided a qualitative picture of the pion's dressed-quark structure.

Derived impact-parameter dependent distribution for the pion.

Abstract

We sketch here an approach to the computation of generalised parton distributions (GPDs), based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, $H_\pi^{\rm v}(x,\xi,t)$. Our analysis focuses on the case of zero skewness, $\xi=0$, and underlines that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for $H_\pi^{\rm v}(x,0,t)$, expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_\pi^{\rm v}(x,0,t)$ and the associated impact-parameter dependent distribution, $q_\pi^{\rm v}(x,|\vec{b}_\perp|)$, which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale.