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

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

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