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

The matrix element squared for Compton scattering of a heavy photon on a longitudinally polarized electron is calculated. The gauge-invariant tensor structure of the heavy photon polarization is considered, assuming that all kinematical invariants and the invariant mass of the heavy photon are large compared with the electron mass. The expressions for the Born and first order radiative corrections are obtained. Applications are discussed.