Beam spin polarization ($P=(N_{+}-N_{-})/(N_{+}+N_{-})$)

A beam's unequal population of spin projections along a specified axis. For spin-one-half particles the displayed longitudinal polarization uses populations parallel and antiparallel to the momentum. An unpolarized beam has equal populations and requires an initial-spin average in a cross section; a polarized beam weights the corresponding helicity amplitudes differently. This differs from photon linear polarization.