We calculate oscillation probabilities in the presence of an external magnetic field in a one-generation neutrino framework that includes both Majorana and Dirac mass terms. First, we write down the Euler-Lagrange equations and obtain a system of eight differential equations coupling together eight different neutrino states that can be distinguished by helicity, chirality, and particle/antiparticle-ness. We then solve this system of differential equations in various special cases, exhibiting different types of oscillations. When the magnetic field is in the direction of momentum, there are only four oscillation channels as helicity flip is forbidden. We observe that chirality flips are suppressed by a factor of m2/E2, whereas the transitions involving active neutrinos and sterile antineutrinos are not while having a form similar to two-generation flavor oscillations.
"Neutrino Oscillations in the Presence of a Magnetic Field,"
Macalester Journal of Physics and Astronomy: Vol. 10:
1, Article 11.
Available at: https://digitalcommons.macalester.edu/mjpa/vol10/iss1/11