  We perform an analysis of the form factors that rule the structure-dependent
amplitude in the radiative pion decay. The resonance contributions to pion -> e
nu_e gamma decays are computed through the proper construction of the vector
and axial-vector form factors by setting the QCD driven asymptotic properties
of the three-point Green functions VVP and VAP, and by demanding the smoothing
of the form factors at high transfer of momentum. A comparison between
theoretical and experimental determinations of the form factors is also carried
out. We also consider and evaluate the role played by a non-standard tensor
form factor. We conclude that, at present and due to the hadronic incertitudes,
the search for New Physics in this process is not feasible.
