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

Abstract

We sketch here an approach to the computation of genaralised 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 v π(x,ξ,t). Our analysis focuses on the case of zero skewness, ξ = 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 v π(x,0,t), expressed as the Radon transform of a single amplitude. Therewith we obtain results for H v π(x,0,t) and the associated impact-parameter dependent distribution, , which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale.