  In this paper we study the generalized electrodynamics contribution for the
electron-positron scattering process, $e^{-}e^{+}\rightarrow e^{-}e^{+}$, the
Bhabha scattering. Within the framework of the standard model, for energies
larger when compared to the electron mass, we calculate the cross section
expression for the scattering process. This quantity is usually calculated in
the framework of the Maxwell electrodynamics and, by phenomenological reasons,
corrected by a cut-off parameter. On the other hand, by considering the
generalized electrodynamics instead of Maxwell's, we can show that the effects
played by the Podolsky mass is actually a natural cut-off parameter for this
scattering process. Furthermore, by means of experimental data of Bhabha
scattering we will estimate its lower bound value. Nevertheless, in order to
have a mathematically well defined description of our study we shall present
our discussion in the framework of the Epstein-Glaser causal theory.
