Chirality-preserving neutrino oscillations in an external magnetic field

Neutrinos propagating in matter acquire an effective electromagnetic vertex induced by their weak interactions with the charged particles in the background. In the presence of an external magnetic field the induced vertex affects the flavor transformations of mixed neutrinos in a way that, in contrast to the oscillations driven by an intrinsic magnetic moment interaction, preserve chirality. We derive the evolution equation for this case and discuss some of the physical consequences in environments such as a supernova. For small values of the square mass difference the resonance for neutrinos and antineutrinos occur within regions which are close. In that case, the resonance condition becomes independent of the vacuum parameters and is approximately the same for both.