  We discuss the role of gravitational corrections to the running of the
electric charge through the evaluation of scattering amplitudes of charged
particles in massless scalar electrodynamics. Computing the complete divergent
part of the S-matrix amplitude for two distinct scattering processes, we show
that quantum gravitational corrections do not alter the running behavior of the
electric charge. Our result does not exclude the possibility that the presence
of a second dimensional constant in the model (a cosmological constant or the
presence of massive particles) could alter this behavior, as was proposed in
earlier works.
