We study the neutrino-photon processes such as $gammagammato ubar{ u}$ and $ ugammato ugamma$ in a background magnetic field smaller than the critical magnetic field $B_cequiv m_e^2/e$. Using Schwingers proper-time method, 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 $m_W$. We briefly discuss the astrophysical implications of our result.
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