Scattering of Polarized Leptons at High Energy

A unified treatment is given of the high-energy elastic and inelastic electromagnetic scattering of electrons and muons by hadrons in terms of the polarization density matrix of the virtual photon exchanged. It is shown that when the leptons are longitudinally polarized, the virtual photon is in a pure polarization state which is a coherent superposition of an elliptically polarized transverse state and a longitudinal state. Experiments utilizing these features are suggested and the formulas for the cross sections are obtained. The limit in which the virtual photon is almost real is investigated carefully. Finally, it is shown that the formalism is immediately applicable to neutrino scattering.