Impact-parameter Dependence of the Diagonal Gpd of the Pion from Chiral Quark Models

We analyze the impact-parameter dependent diagonal non-singlet generalized parton distribution of the pion in two distinct chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model. Leading-order perturbative QCD evolution from the low quark-model scale to higher scales is carried out with the help of the inverse Mellin transform. The model agrees very reasonably with the recent results from transverse-lattice calculations, while the forward parton distribution agrees with the experimental data. This talk is based on our recent work [1], where more details and references can be found. Recently, transverse-lattice calculations have produced first data [2] on the impact-parameter dependent diagonal non-singlet generalized parton distributions (GPD) of the pion (cf. contribution by Dalley). These GPD’s have been a subject of intense studies (for a review and literature see, e.g., Ref. [3, 4]). The impact-parameter (b) formulation, discussed here by Burkardt, is a basis for the transverse lattices [5], as shown by van de Sande. In this talk we present predictions for the GPD of the pion from two chiral quark models: the recently-proposed Spectral Quark Model (SQM) [6] and the Nambu–Jona-Lasinio model with the Pauli-Villars regulator (NJL). Chiral model results for the skewed b-integrated (forward) GPD [7] were shown here by Vento. The off-forward (∆⊥ 6= 0) diagonal (ξ = 0) GPD of the pion (we take π+) is defined as