Effect of beam polarization on two-photon processes

A general treatment of the effect of (transverse or longitudinal) beam polarization on two-photon processes, $e^{+}{e}^{-}\to e^{+}{e}^{-}X$, is given. It is found that the change in the cross section is negligible for most processes including the processes $X={\pi }^0, {\mu }^{+}{\mu }^{-}, \mathrm{and} {\pi }^{+}{\pi }^{-}$.