Generalised Parton Distributions: A Dyson-Schwinger approach for the pion

TL;DR

This paper develops an analytic Dyson-Schwinger approach to compute the pion's Generalised Parton Distribution, aligning well with experimental data and revealing limitations of previous approximations.

Contribution

It introduces an analytic expression for the pion GPD within a Dyson-Schwinger framework, addressing symmetry issues and extending the understanding of pion structure.

Findings

Analytic GPD expression matches experimental data

Identifies symmetry-breaking in impulse approximation

Highlights the Polyakov soft pion theorem

Abstract

We compute the pion quark Generalised Parton Distribution H and quark Double Distributions in a coupled Bethe-Salpeter and Dyson-Schwinger approach in terms of quark flavors or isospin states. We use analytic expressions inspired by the numerical resolution of Dyson-Schwinger and Bethe-Salpeter equations. We obtain an analytic expression for the pion Generalised Parton Distribution at a low scale. Our model fulfils most of the required symmetry properties and compares very well to experimental pion form factor or valence parton distribution function experimental data. In addition, we have highlighted limitations of the so-called impulse approximation, which breaks symmetries when computing the valence parton distribution function. Doing so, we introduced new terms which were neglected before. Finally, we also shed light on a specific property of the pion GPD: Polyakov soft pion theorem.