Neutrino oscillations in accelerated states

We discuss the inverse $\beta$-decay of accelerated protons in the context of neutrino oscillations. The process $p\rightarrow n \ell^+ \nu_\ell$ is kinematically allowed because the accelerating field provides the rest energy difference between initial and final states. The rate of $p\to n$ conversions can be evaluated in either the laboratory frame (where the proton is accelerating) or the co-moving frame (where the proton is at rest and interacts with an effective thermal bath of $\ell$ and $\nu_\ell$ due to the Unruh effect). By explicit calculation, we show the rates in the two frames disagree when taking into account neutrino oscillations, because the weak interaction couples to charge eigenstates whereas gravity couples to neutrino mass eigenstates. The contradiction could be resolved experimentally, potentially yielding new information on the origins of neutrino masses.