A4-based seesaw model for realistic neutrino masses and mixing

Abstract

We present an A4-based model where neutrino masses arise from a combination of see-saw mechanisms. The model is motivated by several small mixing and mass parameters indicated by the data. These are θ 13 , the solar mass splitting, and the small deviation of θ 23 from maximal mixing (= π/4). We take the above as indications that at some level the small quantities are well-approximated by zero. In particular the mixing angles, to a zero order, should be either 0 or π/4. Accordingly, in this model the Type-II see-saw dominates and generates the larger atmospheric mass splitting and sets θ 23 = π/4. The other mixing angles are vanishing as is the solar splitting. We show how the A4 assignment for the lepton doublets leads to this form. We also specify the A4 properties of the right-handed neutrinos which result in a smaller Type-I see-saw contribution that acts as a perturbation and shifts the angles θ 12 and θ 13 into the correct range and the desired value of ∆m 2 solar is produced. The A4 symmetry results in relationships between these quantities as well as with a small deviation of θ 23 from π/4. If the right-handed neutrino mass matrix, M R , is chosen real then there is no leptonic CP-violation and only Normal Ordering is admissible. If M R is complex then Inverted Ordering is also allowed with the proviso that the CP-phase, δ, is large, i.e., ∼ π/2 or −π/2. The preliminary results from NOνA favouring Normal Ordering and δ near −π/2 imply quasi-degenerate neutrino masses in this model. PACS No:14.60.Pq Key Words: Neutrino mixing, θ 13 , Solar splitting, A4, see-saw I IntroductionMany neutrino oscillation experiments have established that neutrinos are massive and non-degenerate and that the flavour eigenstates are not identical with the mass eigenstates. For the three neutrino paradigm the two independent mass square splittings are the solar (∆m 2 solar ) and the atmospheric (∆m 2 atmos ). The mass and flavour bases are related through the Pontecorvo, Maki, Nakagawa, Sakata -PMNS -matrix usually parametrized as: where c ij = cos θ ij and s ij = sin θ ij .The recent measurement of a non-zero value for θ 13 [1], which is small compared to the other mixing angles, has led to a flurry of activity in developing neutrino mass models which incorporate this feature. Earlier we had demonstrated [2] that a direction which bears exploration is whether two small quantities * email: soumitapramanick5@gmail.com † email: palitprof@gmail.com 1 in the neutrino sector, namely, θ 13 and the ratio, R ≡ ∆m 2 solar /∆m 2 atmos , could in fact be related to each other, both resulting from a small perturbation. Subsequently we had shown [3] that it is possible to envisage scenarios where only the larger ∆m 2 atmos and θ 23 = π/4 are present in a basic structure of neutrino mass and mixing and the rest of the quantities, namely, θ 13 , θ 12 , the deviation of θ 23 from π/4, and ∆m 2 solar all have their origin in a smaller see-saw induced perturbation 1 . Obviously, this gets reflected in constraints on the measured quantitie...

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