Dirac CP phases in a 3 + 1 neutrino scenario with $$\mu -\tau $$ symmetry

A sterile neutrino in the $$3+1$$ 3 + 1 scheme, where the sterile accounts for neutrino anomalies not explained solely by the weak active neutrinos, arises as a natural source for the breaking of the $$\mu -\tau $$ μ - τ symmetry suggested by oscillation neutrino data. We explore the predictions for the Dirac CP phases in this scenario, with and without sterile neutrino decay, and show that current limits on $$\delta _{CP}$$ δ CP suggest a normal hierarchy and a lightest neutrino scale below 0.1 eV as the most plausible explanation for that, when Majorana phases are null. Other Dirac phases turn out to be non zero as well.

Aspects of high scale leptogenesis with low-energy leptonic CP violation

Using the density matrix equations (DME) for high scale leptogenesis based on the type I seesaw mechanism, in which the CP violation (CPV) is provided by the low-energy Dirac or/and Majorana phases of the neutrino mixing (PMNS) matrix, we investigate the 1-to-2 and the 2-to-3 flavour regime transitions, where the 1, 2 and 3 leptogenesis flavour regimes in the generation of the baryon asymmetry of the Universe ηB are described by the Boltzmann equations. Concentrating on the 1-to-2 flavour transition we determine the general conditions under which ηB goes through zero and changes sign in the transition. Analysing in detail the behaviour of ηB in the transition in the case of two heavy Majorana neutrinos N1,2 with hierarchical masses, M1 ≪ M2, we find, in particular, that i) the Boltzmann equations in many cases fail to describe correctly the generation of ηB in the 1, 2 and 3 flavour regimes, ii) the 2-flavour regime can persist above (below) ∼ 1012 GeV (∼ 109 GeV), iii) the flavour effects in leptogenesis persist beyond the typically considered maximal for these effects leptogenesis scale of 1012 GeV. We further determine the minimal scale M1min at which we can have successful leptogenesis when the CPV is provided only by the Dirac or Majorana phases of the PMNS matrix as well as the ranges of scales and values of the phases for having successful leptogenesis. We show, in particular, that when the CPV is due to the Dirac phase δ, there is a direct relation between the sign of sin δ and the sign of ηB in the regions of viable leptogenesis in the case of normal hierarchical light neutrino mass spectrum; for the inverted hierarchical spectrum the same result holds for M1 ≲ 1013 GeV. The considered different scenarios of leptogenesis are testable and falsifiable in low-energy neutrino experiments.

A hybrid seesaw model and hierarchical neutrino flavor structures based on A4 symmetry

We propose a hybrid seesaw model based on A4 flavor symmetry, which generates a large hierarchical flavor structure. In our model, tree-level and one-loop seesaw mechanisms predict different flavor structures in the neutrino mass matrix, and generate a notable hierarchy among them. We find that such a hierarchical structure gives a large effective neutrino mass which can be accessible by next-generation neutrinoless double beta decay experiments. Majorana phases can also be predictable. The A4 flavor symmetry in the model is spontaneously broken to the Z2 symmetry, leading to a dark matter candidate which is assumed to be a neutral scalar field. The favored mass region of the dark matter is obtained by numerical computations of the relic abundance and the cross section of the nucleon. We also investigate the predictions of the several hierarchical flavor structures based on A4 symmetry for the effective neutrino mass and the Majorana phases, and find the characteristic features depending on the hierarchical structures.