Neutrino Annihilation in Stellar Magnetic Fields

The potential enhancement of the cross section $\nu\bar\nu\to e^+e^-$ in the presence of a magnetic field is of critical interest for the study of supernovae and as a possible mechanism for gamma ray bursts. While parity violation(PV) in this reaction in free space is forbidden by CP, the presence of a CP non-invariant background gas of electrons creates an asymmetry in the cross section which may contribute to the asymmetry of a supernova and the natal velocities of neutron stars. We calculate the cross section in the presence of fields as high as $B = 10^{16}$G and find no significant enhancement of the cross section with magnetic field strength. By studying the systematics of our results as a function of environmental variables(field strength, density,temperature), we extrapolate the relative strength of the parity violating terms to the weak field limit, and find the parity violation is insufficient to provide the ``kick'' required to explain the observed velocities of neutron stars.