Cyclic symmetry in the neutrino sector with the type-I seesaw mechanism in the mass basis of charged leptons and right chiral neutrinos (N iR , i = e, µ, τ ) generates two fold degenerate light neutrino and three fold degenerate heavy neutrino mass spectrum. Consequently, such scheme, produces vanishing one light neutrino mass squared difference and lepton asymmetry. To circumvent such unphysical outcome, we break cyclic symmetry in the diagonal right chiral neutrino mass term by a small breaking parameter. Nonzero mass squared differences and mixing angles are generated with the help of the small breaking parameter. Smallness of the breaking parameter opens up a possibility of resonant leptogenesis. Assuming complex Yukawa couplings, we derive generalized expressions flavor dependent CP asymmetry parameters (ε α i ) which are valid for quasi degenerate as well as hierarchical mass spectrum of right handed neutrinos. There after we set up the chain of coupled Boltzmann equations (which are flavor dependent too) which have to be solved in order to get the final lepton asymmetries. Depending upon the temperature regime the CP asymmetries and the Boltzmann equations may also be flavor independent. As our goal is to study the enhancement of CP asymmetry due to quasi degeneracy of right handed neutrinos, we select only the lowest allowed (by neutrino oscillation data) value of breaking parameter (and other corresponding Lagrangian parameters) and estimate the baryon asymmetry parameter Y B . Experimental constraint of Y B introduces a bound on right handed neutrino mass which remained unrestricted by neutrino oscillation data. *
We investigate 'Scaling ansatz' in the neutrino sector within the framework of type I seesaw mechanism with diagonal charged lepton and right handed Majorana neutrino mass matrices (M R ).We also assume four zero texture of Dirac neutrino mass matrices (m D ) which severely constrain the phenomenological outcomes of such scheme. Scaling ansatz and the present neutrino data allow only Six such matrices out of 126 four zero Yukawa matrices. In this scheme, in order to generate large θ 13 we break scaling ansatz in m D through a perturbation parameter and we also show our breaking scheme is radiatively stable. We further investigate CP violation and baryogenesis via leptogenesis in those surviving textures.
Baryogenesis via leptogenesis is investigated in a specific model of light neutrino masses and mixing angles. The latter was proposed on the basis of an assumed complex-extended scaling property of the neutrino Majorana mass matrix M ν , derived with a type-1 seesaw from a Dirac mass matrix m D and a heavy singlet neutrino Majorana mass matrix M R . One of its important features, highlighted here, is that there is a common source of the origin of a nonzero θ 13 and the CP violating lepton asymmetry through the imaginary part of m D . The model predicted CP violation to be maximal for the Dirac type and vanishing for the Majorana type. We assume strongly hierarchical mass eigenvalues for M R . The leptonic CP asymmetry parameter ε α 1 with lepton flavor α, originating from the decays of the lightest of the heavy neutrinos N 1 (of mass M 1 ) at a temperature T ∼ M 1 , is what matters here with the lepton asymmetries, originating from the decays of N 2,3 , being washed out. The light leptonic and heavy neutrino number densities (normalized to the entropy density) are evolved via Boltzmann equations down to electroweak temperatures to yield a baryon asymmetry through sphaleronic transitions. The effects of flavored vs. unflavored leptogenesis in the three mass regimes (1) M 1 < 10 9 GeV, (2) 10 9 GeV < M 1 < 10 12 GeV and (3) M 1 > 10 12 GeV are numerically worked out for both a normal and an inverted mass ordering of the light neutrinos. Corresponding results on the baryon asymmetry of the universe are obtained, displayed and discussed. For values close to the best-fit points of the input neutrino mass and mixing parameters, obtained from neutrino oscillation experiments, successful baryogenesis is achieved for the mass regime (2) and a normal mass ordering of the light neutrinos with a nonzero θ 13 playing a crucial role. However, the other possibility of an inverted mass ordering for the same mass regime, though disfavored, cannot be excluded. A discussion is also given on the sensitivity of our result to the masses M 2,3 of the heavier neutrinos N 2,3 .
We use S 4 discrete group to construct a neutrino flavour model which leads to T M 1 mixing and is consistent with the neutrino oscillation data. Using the model's constrained parameter space, we predict the values of Dirac CP phase and the light neutrino mass as −1 < sin δ < −0.9 and 1.7 < m 1 (meV) < 5.5 respectively. We thoroughly examine the usefulness of this model in explaining the observed baryon asymmetry of the Universe. Near-maximal breaking of CP symmetry (arising due to the TM 1 constraint) helps us in generating adequate baryon asymmetry through leptogenesis. We study the evolution of the asymmetry (generated due to the decay of the heavy Majorana neutrinos) starting from the primordial Universe in two different ways (i)explicitly solving network of Boltzmann equations, (ii) using approximate analytic solution and we have shown the extent of their equivalence. Nearly accurate analytical fits are used thereafter to evaluate baryon asymmetry for the whole parameter space allowed by 3σ global fit of oscillation data and to impose a constraint on the yet unbounded mass scale parameter of Dirac neutrino mass matrix. Furthermore, significant contribution of N 2 decay in the context of flavoured leptogenesis is also estimated.
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