Incoherent pair background processes with full polarizations at the ILC

Incoherent background pair production processes are studied with respect to full polarizations of all states. Real initial photon polarizations are obtained via a QED calculation of the beamstrahlung process. Virtual photon polarizations are related to the electric field of the colliding bunches at the point of pair production. An explicit expression for the virtual photon polarization vector is developed and found to have no circular polarization component. Pair polarization states are highly dependent on initial state circular polarization and are consequently produced almost unpolarized. The Breit-Wheeler cross-section with full polarizations is calculated and coded into the CAIN pair generator program. Numerical evaluations of the ILC, operating with the seven proposed collider parameter sets, shows that there are 10 - 20% less low energy pairs than previously thought. Collider luminosity, as calculated by CAIN, remains the same.