Relativistic quantum mechanics of massive neutrinos in a rotating frame

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Abstract
We study the evolution of neutrinos electroweakly interacting with a rotating matter. The description of neutrinos is based on the Dirac equation in the corotating noninertial frame where matter is at rest. We find the solution of this Dirac equation, where the matter angular velocity is accounted for exactly, for massless neutrinos. In case of massive particles, this solution is obtained for a slowly rotating matter. Our findings are compared with previous research. We consider two applications of our results. First, we compute the electroweak contribution to the vector current of neutrinos along the rotation axis, which is analogous to the chiral vortical effect. This current is shown to be nonzero for both massless and massive particles. Then, we take into account the nonzero mixing between different mass eigenstates. It allows us to study neutrino flavor oscillations in rotating matter and account for noninertial effects. We derive the transition probability which reveals the resonance. These findings generalize the description of neutrino oscillations in a nonmoving matter. Some astrophysical applications are briefly discussed.
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