Abstract
Dirac neutrino masses require two distinct neutral Weyl spinors per generation, with a special arrangement of masses and interactions with charged leptons. Once this arrangement is perturbed, lepton number is no longer conserved and neutrinos become Majorana particles. If these lepton number violating perturbations are small compared to the Dirac mass terms, neutrinos are quasi-Dirac particles. Alternatively, this scenario can be characterized by the existence of pairs of neutrinos with almost degenerate masses, and a lepton mixing matrix which has 12 angles and 12 phases. In this work we discuss the phenomenology of quasi-Dirac neutrino oscillations and derive limits on the relevant parameter space from various experiments. In one parameter perturbations of the Dirac limit, very stringent bounds can be derived on the mass splittings between the almost degenerate pairs of neutrinos. However, we also demonstrate that with suitable changes to the lepton mixing matrix, limits on such mass splittings are much weaker, or even completely absent. Finally, we consider the possibility that the mass splittings are too small to be measured and discuss bounds on the new, non-standard lepton mixing angles from current experiments for this case.
Highlights
Neutrino oscillation experiments cannot distinguish Dirac from Majorana neutrinos, it is still unknown whether or not lepton number is conserved
Let us turn our attention to a generic mixing matrix Ω with dimensions n × m. Such a matrix can be described by 2nm real numbers, yet orthonormality of rows (ΩΩ† 1⁄4 1) imposes n2 conditions on them, and it is possible to absorb n phases into the charged lepton fields, there is a total of nð2m − n − 1Þ real physical degrees of freedom in Ω
If the lepton number violating mass terms are smaller than the lepton number preserving ones, neutrinos are quasi-Dirac particles
Summary
Neutrino oscillation experiments cannot distinguish Dirac from Majorana neutrinos, it is still unknown whether or not lepton number is conserved. QUASI-DIRAC NEUTRINO OSCILLATIONS more than one oscillation probability, constraints can only be derived for certain combinations of angles and phases of the mixing matrix We prefer to define quasi-Dirac (QD) neutrinos as being a mixture of active and sterile states, in contrast with pseudo-Dirac (PD) neutrinos which are composed of active states only In both cases, the structure of mass and mixing matrices must be such that the lepton sector is close to preserving one or more Uð1Þ symmetries. Are usually derived assuming best fit point values for the standard oscillation parameters, to which two new parameters (one angle and one mass splitting) are added in the fit This approach does not cover the general quasi-Dirac neutrino parameter space.
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