Abstract
We study the non-relativistic limit of Dirac equation for mixed neutrinos. We demonstrate that such a procedure inevitably leads to a redefinition of the inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for neutrinos with definite flavor. We then show that, when a gravitational interaction is switched on, in the weak-field approximation the mass parameter which couples to gravity (gravitational mass) does not undergo the same reformulation as the inertial mass, thus leading to an apparent breakdown of the weak equivalence principle.
Highlights
Neutrino physics has long been considered as an important playground for testing the weak equivalence principle (WEP) both theoretically and experimentally [1,2,3]
By restricting our analysis of neutrino mixing to non-relativistic quantum mechanics (QM), we find that novel and intriguing effects related to the notion of inertial mass arise in the flavor basis even without invoking the full quantum field theoretical (QFT) apparatus
This Letter is organized as follows: in Section 2, we study in detail the non-relativistic limit of the Dirac equation for mixed neutrinos and show that in this framework one inevitably comes across a non-trivial correction to the inertial mass mi
Summary
Neutrino physics has long been considered as an important playground for testing the weak equivalence principle (WEP) both theoretically and experimentally [1,2,3]. With the infusion of new ideas from particle cosmology and astrophysics and the advent of a high precision instrumentation, the behavior of non-relativistic neutrinos has recently been studied from various standpoints These particles can exhibit novel features when flavor oscillations are properly accounted for [13], and their presence can represent a direct evidence for the existence of cold dark matter [14]. We are interested in the non-relativistic behavior of such states In this connection, it should be pointed out that, in such a case, corrections to the usual oscillation formula arise when a full-fledged field theoretical approach to neutrino mixing is performed [30]. In the Appendix, some finer technical and conceptual details needed in the main text are clarified
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