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Towards a Pion Generalized Parton Distribution Model from Dyson-Schwinger Equations

We compute the pion quark Generalized Parton Distribution H and quark Double Distributions F and G in a coupled Bethe-Salpeter and Dyson-Schwinger approach in terms of quark flavors or isospin states. We use simple analytic expressions inspired by the numerical resolution of Dyson-Schwinger and Bethe-Salpeter equations. We explicitly check the support and polynomiality properties, and the behavior under charge conjugation or time invariance of our model. We obtain analytic expressions for the pion Double Distributions and Generalized Parton Distribution at vanishing pion momentum transfer at a low scale. Our model compares very well to experimental pion form factor or Parton Distribution Function data. This paper is the first stage of a GPD-modeling program which will be pursued by incorporating more realistic solutions of the Bethe-Salpeter and Dyson-Schwinger equations.