Flavored leptogenesis with quasi degenerate neutrinos in a broken cyclic symmetric model

Cyclic symmetry in the neutrino sector with the type-I seesaw mechanism in the mass basis of charged leptons and right chiral neutrinos ($N_{iR}$, $i=e,mu,tau$) 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 ($varepsilon^alpha_i$) 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.

Maximal zero textures of the inverse seesaw with broken $mutau$ symmetry

The inverse neutrino seesaw, characterised by only one source of lepton number violation at an ultralight $O$(keV) scale and observable new phenomena at TeV energies accessible to the LHC, is considered. Maximal zero textures of the $3times 3$ lighter and heavier Dirac mass matrices of neutral leptons, appearing in the Lagarangian for such an inverse seesaw, are studied within the framework of $mutau$ symmetry in a specified weak basis. That symmetry ensures the identity of the positions of maximal zeros of the heavy neutrino mass matrix and its inverse. It then suffices to study the maximal zeros of the lighter Dirac mass matrix and those of the inverse of the heavier one since they come in a product. The observed absence of any unmixed neutrino flavour and the assumption of no strictly massless physical neutrino state allow only eight $4$-zero $times$ $4$-zero, eight $4$-zero $times$ $6$-zero and eight $6$-zero $times$ $4$-zero combinations. The additional requirement of leptogenesis is shown to eliminate the last sixteen textures. The surviving eight $4$-zero $times$ $4$-zero textures are subjected to the most general explicit $mutau$ symmetry breaking terms in the Lagrangian in order to accommodate the nonzero value of $theta_{13}$ in the observed range. A full diagonalisation is then carried out. On numerical comparison with all extant and relevant neutrino (antineutrino) data, seven of these eight combination textures in five neutrino matrix forms are found to be allowed, leading to five distinct neutrino mass matrices. Two of these permit only a normal (and the other three only an inverted) mass ordering of the light neutrinos.

Neutrino Yukawa textures within type-I see-saw

The arbitrariness of Yukawa couplings can be reduced by the imposition of some flavor symmetries and/or by the realization of texture zeros. We review neutrino Yukawa textures with zeros within the framework of the type-I seesaw with three heavy right chiral neutrinos and in the basis where the latter and the charged leptons are mass diagonal. An assumed non-vanishing mass of every ultralight neutrino and the observed non-decoupling of any neutrino generation allow a maximum of four zeros in the Yukawa coupling matrix $Y_ u$ in family space. There are seventy two such textures. We show that the requirement of an exact $mutau$ symmetry, coupled with the observational constraints, reduces these seventy two allowed textures to only four corresponding to just two different forms of the light neutrino mass matrix $M_{ u A}/M_{ u B}$, resulting in an inverted/normal mass ordering. The effect of each of these on measurable quantities can be described, apart from an overall factor of the neutrino mass scale, in terms of two real parameters and a phase angle all of which are within very constrained ranges. The masses and Majorana phases of ultralight neutrinos are predicted within definite ranges with $3sigma$ laboratory and cosmological observational inputs. The rate for $0 ubetabeta$ decay, though generally below the reach of planned experiments, could approach it in some parameteric regions. Within the same framework, we also study Yukawa textures with a fewer number of zeros, but with exact $mutau$ symmetry. We further formulate the detailed scheme of the explicit breaking of $mutau$ symmetry in terms of three small parameters for allowed four zero textures. The observed sizable mixing between the first and third generations of neutrinos is shown to follow for a suitable choice of these symmetry breaking parameters.