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

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, $H_{\pi }^{\mathrm{v}}(x,\xi ,t)$. 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 $H_{\pi }^{\mathrm{v}}(x,0,t)$, expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_{\pi }^{\mathrm{v}}(x,0,t)$ and the associated impact-parameter dependent distribution, $q_{\pi }^{\mathrm{v}}(x,|{\vec{b}}_{\perp }|)$, which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale.

Comments: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2014); CNUM: C14-12-02.1