Interplay of nonrelativistic and relativistic effects in neutrino oscillations

A theoretical structure that involves neutrino mass eigenstates at nonrelativistic as well as relativistic energies is presented. Using this framework, we find that if the particle $X$, with a mass $33.9$ MeV, of the KARMEN Collaboration anomaly is identified with the third neutrino mass eigenstate, then the present limit of $23$ MeV upper bound on the $\tau$ neutrino mass implies $|U_{\tau 3}|<0.82\mathrm{}$.