Cherenkov radiation by neutrinos

We discuss the Cherenkov process $\nu\to\nu\gamma$ in the presence of a homogeneous magnetic field. The neutrinos are taken to be massless with only standard-model couplings. The magnetic field fulfills the dual purpose of inducing an effective neutrino-photon vertex and of modifying the photon dispersion relation such that the Cherenkov condition $\omega<|{\bf k}|$ is fulfilled. For a field strength $B_{\rm crit}=m_e^2/e=4.41\times10^{13} Gauss$ and for $E=2m_e$ the Cherenkov rate is about $6\times10^{-11}s^{-1}$.