  The transverse beam spin induced asymmetry is calculated for the scattering
of transversally polarized electrons on a proton target within a realistic
model. Such asymmetry is due to the interference between the Born amplitude and
the imaginary part of two photon exchange amplitude. In particular, the
contribution of non-excited hadron state (elastic) to the two photon amplitude
is calculated. The elastic contribution requires infrared divergences
regularization and can be expressed in terms of numerical integrals of the
target form factor. The inelastic channel corresponding to the one pion
hadronic state contribution is enhanced by squared logarithmic terms. We show
that the ratio of elastic over inelastic channel is of the order of 0.3 and
cannot be ignored. Enhancement effects due to the decreasing of form factors
bring the transverse beam asymmetry to values as large as $10^{-4}$ for
particular kinematical conditions.
