Neutrino survival probabilities in magnetic fields

We show that, for Majorana neutrinos propagating in a constant magnetic field, the flavour survival probabilities for left-handed neutrinos is the same as for right-handed neutrinos, i.e., $P^M (\nu_{\alpha L}\to\nu_{\alpha L}) = P^M (\nu_{\alpha R}\to\nu_{\alpha R})$, where $\alpha = e, \mu, \tau$, whereas in the Dirac case the corresponding probabilities $P^D (\nu_{\alpha L}\to\nu_{\alpha L})$ and $P^D (\bar\nu_{\alpha R}\to\bar\nu_{\alpha R})$ are in general different. This might lead to a novel way to search for the nature of neutrinos. We also discuss how this relation for Majorana neutrinos gets modified when the magnetic field is not constant. However, if matter effects become important the relation does not hold anymore.