Neutrino-photon scattering and its crossed processes in a background magnetic field

We study the neutrino-photon processes such as γγ→νν̄, νγ→νγ, and νν̄→γγ in a background magnetic field smaller than the critical magnetic field Bc≡me2/e. Using Schwingerʹs formalism, we extract leading magnetic-field contributions to the above processes. Our result is valid throughout the kinematic regime where both neutrino and photon energies are significantly smaller than mW. We briefly discuss the astrophysical implications of our result.