Cherenkov radiation by massless neutrinos in a magnetic field

We calculate the Cherenkov process ν→νγ in the presence of a homogeneous magnetic field. The neutrinos are taken to be massless with only standard-model couplings. The magnetic field satisfies the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation such that the Cherenkov condition ω<|k| is satisfied. Our effect is closely related to photon splitting that occurs in magnetic fields and that may be astrophysically important in the strong magnetic fields of pulsars. It is also closely related to magnetic-field enhanced radiative decays ν→ν^'γ that have been extensively discussed in the recent literature. In the appropriate limits we agree with these results, but we disagree with earlier explicit calculations of the Cherenkov process. For a field strength Bcrit=mₑ²/e=4.41×10¹³ G and for E=2mₑ the Cherenkov rate is about 6×10^-11 s^-1 and thus too small to be of practical importance for pulsar physics.