The Pion-Photon Transition Distribution Amplitudes in the Nambu-Jona Lasinio Model

We define the pion-photon Transition Distribution Amplitudes (TDA) in a field theoretic formalism from a covariant Bethe-Salpeter approach for the determination of the bound state. We apply our formalism to the Nambu - Jona Lasinio model, as a realistic theory of the pion. The obtained vector and axial TDAs satisfy all features required by general considerations. In particular, sum rules and polynomiality condition are explicitly verified. We have numerically proved that the odd coefficients in the polynomiality expansion of the vector TDA vanish in the chiral limit. The role of PCAC and the presence of a pion pole are explicitly shown.