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

Abstract

The (inverse) β -decay of uniformly accelerated protons (p → n + e + + ν 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.

On the very nature of neutrinos: the $\beta$-decay as a test bench

“…2 Apart from its intrinsic interest in some astrophysical situations as, e.g., the cooling of neutron stars, where significant accelerations can be provided by internal magnetic fields, we remark that this study is intended as a "stress-test" of the formalism of Refs. [2,6,7]. In the limit of vanishing acceleration, indeed, we prove that the obtained decay rate recovers the standard expression for static neutrons, thus providing a check for the internal consistency of the formalism of Refs.…”

“…As explained in Ref. [7], this is related to the conservation of the total lepton number both in the presence and in the absence of flavor mixing.…”

“…In the limit of vanishing acceleration, indeed, we prove that the obtained decay rate recovers the standard expression for static neutrons, thus providing a check for the internal consistency of the formalism of Refs. [2,6,7], as well as for the results there contained. We finally discuss the relevance of our outcome to some recent neutrino experiments such as KATRIN and PTOLEMY.…”

“…In a series of recent works [1,2,3,4,5,6,7], the inverse β -decay of uniformly accelerated protons, p → n + e + + ν e , has served as a theoretical tool for testing the very nature of asymptotic neutrino states -mass or flavor. By computing the scalar decay rate both in the laboratory frame (where the proton is accelerated) and in the comoving frame (where the proton is at rest and interacts with the Unruh [8] thermal bath of electrons and antineutrinos), it has been shown that the only way to get consistency with: i) the general covariance of Quantum Field Theory (QFT) [2], ii) the phenomenon of neutrino oscillations [6] and iii) the related effects of CP violation [7] is by use of flavor states. However, due to the lack of feasible experiments 1 and the widespread skepticism on the realness of Unruh effect, one may question the physical relevance of the above framework and the results it entails [4].…”

“…The above analysis is later generalized to accelerated neutrons by using the semiclassical treatment of Refs. [2,6,7]. 2 Apart from its intrinsic interest in some astrophysical situations as, e.g., the cooling of neutron stars, where significant accelerations can be provided by internal magnetic fields, we remark that this study is intended as a "stress-test" of the formalism of Refs.…”