On the $$\beta $$-decay of the accelerated proton and neutrino oscillations: a three-flavor description with CP violation

The (inverse) $$\beta $$-decay of uniformly accelerated protons ($$p\rightarrow n+ e^{+}+\nu _e$$) has been recently analyzed in the context of two-flavor neutrino mixing and oscillations. It has been shown that the decay rates as measured by an inertial and comoving observer are in agreement, provided that: (i) the thermal nature of the accelerated vacuum (Unruh effect) is taken into account; (ii) the asymptotic behavior of neutrinos is described through flavor (rather than mass) eigenstates; (iii) the Unruh radiation is made up of oscillating neutrinos. Here we extend the above considerations to a more realistic scenario including three generations of Dirac neutrinos. By following the outlined recipe, we find that the equality between the two rates still holds true, confirming that mixing is perfectly consistent with the General Covariance of Quantum Field Theory. Notably, we prove that the analysis of CP violation in neutrino oscillations provides a further solid argument for flavor states as fundamental representation of asymptotic neutrino states. Our approach is finally discussed in comparison with the other treatments appeared in literature.