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Transition distribution amplitudes (TDAs) are non-perturbative quantities appearing in the description of certain exclusive processes, for instance hadron-anti-hadron annihilation HH → γ*γ or backward virtual Compton scattering. They are similar to generalized parton distributions (GPDs), except that the non-diagonality concerns not only the momenta, but also the physical states (they are defined in terms of hadron-photon matrix element of a non-local operator). For the case of hadronic states such as pions, there are two TDAs of interest: the vector and the axial one. They are straightforwardly related to the axial and vector form factors controlling weak pion decays π± → e±νγ. The value at zero momentum transfer of the vector form factor is fixed by the axial anomaly, while this is not the case for the axial one. Moreover, the vector form factor is related to the pion-photon transition form factor which was recently measured by Belle and BaBar giving contradictory results at high momentum transfers. We have studied pion-to-photon TDAs within the non-local chiral quark model using modified non-local currents satisfying Ward-Takahashi identities. We found that the value of the axial form factor at zero momentum transfer is shifted towards the experimental value due to the non-locality of the model (in the local quark models the values of both vector and axial form factors at zero momentum transfer are the same, what is not consistent with the data). We also calculate the pion-photon transition form factor and compare it with the data

Pion-to-photon transition distribution amplitudes and related form factors in the non-local chiral quark model