Compton tensor with heavy photon in the case of a longitudinally polarized fermion

The matrix element squared for Compton scattering of a heavy photon on a longitudinally polarized electron is calculated. Assuming that all kinematical invariants and the invariant mass of the heavy photon are large in comparison with the electron mass, the gauge-invariant tensor structure of the heavy photon polarization is considered. The expressions of the Born cross section and first order radiative corrections are obtained. Possible applications for current and future polarization experiments in deep inelastic scattering are briefly discussed.