A Nakanishi-based model illustrating the covariant extension of the pion GPD overlap representation and its ambiguities

A systematic approach for the model building of Generalized Parton Distributions (GPDs), based on their overlap representation within the DGLAP kinematic region and a further covariant extension to the ERBL one, is applied to the valence-quark pion’s case, using light-front wave functions inspired by the Nakanishi representation of the pion Bethe–Salpeter amplitudes (BSA). This simple but fruitful pion GPD model illustrates the general model building technique and, in addition, allows for the ambiguities related to the covariant extension, grounded on the Double Distribution (DD) representation, to be constrained by requiring a soft-pion theorem to be properly observed.The authors would like to thank J-F. Mathiot, C.D. Roberts, G. Salme and C. Shi for valuable discussions and comments. This work is partly supported by the Commissariat a l'Energie Atomique et aux Energies Alternatives, the GDR QCD "Chromodynamique Quantique", the ANR-12-MONU-0008-01 "PARTONS" and the Spanish ministry Research Project FPA2014-53631-C2-2-P