DSE inspired model for the pion's valence dressed-quark GPD. (July 2015) - Chang, L; Mezrag, C; Moutarde, H; Roberts, C D; Rodríguez-Quintero, J; Sabatié, F
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.