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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., Comment: 36 pages, 9 figures, 16 tables (Accepted for publication in Physical Review D)

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 $3\times 3$ lighter and heavier Dirac mass matrices of neutral leptons, appearing in the Lagarangian for such an inverse seesaw, are studied within the framework of $\mu\tau$ 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 $\mu\tau$ 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., Comment: 20 pages, no figure, published in Indian Journal of Physics (Special issue commemorating the 125th birth anniversary of C.~V.~Raman)

General Majorana neutrino mass matrix is complex symmetric and for three generations of neutrinos it contains 12 real parameters. We diagonalize this general neutrino mass matrix and express the three neutrino masses, three mixing angles, one Dirac CP phase and two Majorana phases (removing three unphysical phases) in terms of the neutrino mass matrix elements. We apply the results in the context of a neutrino mass matrix derived from a broken cyclic symmetry invoking type-I seesaw mechanism. Phenomenological study of the above mass matrix allows enough parameter space to satisfy the neutrino oscillation data with only 10% breaking of this symmetry. In this model only normal mass hierarchy is allowed. In addition, the Dirac CP phase and the Majorana phases are numerically estimated. $\Sigma m_i$ and $|m_{\nu_{ee}}|$ are also calculated., Comment: 24 pages, 3 figures

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 $Y_\nu$ in family space. There are seventy two such textures. We show that the requirement of an exact $\mu\tau$ 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 $M_{\nu A}/M_{\nu B}$, 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 $3\sigma$ laboratory and cosmological observational inputs. The rate for $0\nu\beta\beta$ 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 $\mu\tau$ symmetry. We further formulate the detailed scheme of the explicit breaking of $\mu\tau$ 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., Comment: invited review article, to appear in a special issue on neutrinos in the journal Advances in High Energy Physics (AHEP)

Within the type-I seesaw and in the basis where charged lepton and heavy neutrino mass matrices are real and diagonal, $\mu\tau$ symmetric four and three zero neutrino Yukawa textures are perturbed by lowest order $\mu\tau$ symmetry breaking terms. These perturbations are taken to be the {\it most general ones for those textures}. For quite small values of those symmetry breaking parameters, permitting a lowest order analysis, current best-fit ranges of neutrino mass squared differences and mixing angles are shown to be accommodable, including a value of $\theta_{13}$ in the observed range, provided all the light neutrinos have an inverted mass ordering., Comment: 20 pages, 8 figures, published version with considerable elaboration

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 $\theta_{13}$ 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., Comment: 25 pages, 8 figures, Accepted for publication in Phys. Rev. D

Four zero neutrino Yukawa textures in a specified weak basis, combined with $\mu\tau$ symmetry and type-I seesaw, yield a highly constrained and predictive scheme. Two alternately viable $3\times3$ light neutrino Majorana mass matrices $m_{\nu A}/m_{\nu B}$ result with inverted/normal mass ordering. Neutrino masses, Majorana in character and predicted within definite ranges with laboratory and cosmological inputs, will have their sum probed cosmologically. The rate for $0\nu\beta\beta$ decay, though generally below the reach of planned experiments, could approach it in some parameter region. Departure from $\mu\tau$ symmetry due to RG evolution from a high scale and consequent CP violation, with a Jarlskog invariant whose magnitude could almost reach $6\times 10^{-3}$, are explored., Comment: Published version

The generation of the right amount of baryon asymmetry $\eta$ of the Universe from supersymmetric leptogenesis is studied within the type-I seesaw framework with three heavy singlet Majorana neutrinos $N_i\,\,(i = 1,2,3)$ and their superpartners. We assume the occurrence of four zeroes in the neutrino Yukawa coupling matrix $Y_\nu$, taken to be $\mu\tau$ symmetric, in the weak basis where $N_i$ (with real masses $M_i>0$) and the charged leptons $l_\alpha\,\, (\alpha = e,\mu,\tau)$ are mass diagonal. The quadrant of the single nontrivial phase, allowed in the corresponding light neutrino mass matrix $m_\nu$, gets fixed and additional constraints ensue from the requirement of matching $\eta$ with its observed value. Special attention is paid to flavor effects in the washout of the lepton asymmetry. We also comment on the role of small departures from high scale $\mu\tau$ symmetry due to RG evolution., Comment: 35 pages, no figure, Published Version

Within the type-I seesaw framework with three heavy right chiral neutrinos and in the basis where the latter and the charged leptons are mass diagonal, a near `mu-tau' symmetry in the neutrino sector is strongly suggested by the neutrino oscillation data. There is further evidence for a close to the tribimaximal mixing pattern which subsumes `mu-tau' symmetry. On the other hand, the assumption of a (maximally allowed) four zero texture in the Yukawa coupling matrix Y_nu in the same basis leads to a highly constrained and predictive theoretical scheme. We show that the requirement of an exact `mu-tau' symmetry, coupled with observational constraints, reduces the `seventy two' allowed textures in such a `Y_nu' to 'only four' corresponding to just two different forms of the light neutrino mass matrix `m_nu'. 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 additional input of a tribimaximal mixing reduces these three parameters to `only one' with a very nearly fixed value. Implications for both flavored and unflavored leptogenesis as well as radiative lepton flavor violating decays are discussed. We also investigate the stability of these conclusions under small deviations due to renormalization group running from a high scale where the four zero texture as well as `mu-tau' symmetry or the tribimaximal mixing pattern are imposed., Comment: Typographical changes,accepted for publication in JHEP

We have shown that non-zero U_{e3} is generated in a see-saw type softly broken A_4 symmetric model through a single parameter perturbation in m_D in a single element. We have explored all possible 9 cases to study the neutrino mixing angles considering the best fitted values of \Delta m_{\odot}^2 and \Delta m_{atm}^2 with all parameters real. We have extended our analysis for the complex case and demonstrated large low energy CP violation (J_{CP}\simeq 10^{-2}) and m_{ee} in addition to mixing and mass pattern. We have also investigated leptogenesis and for a reasonable choice of model parameters compatible with low energy data, WMAP value of baryon asymmetry 6\times 10^{-10} is obtained for right handed neutrino mass scale M_0\simeq 10^{13} GeV. We have obtained a relation among the phases responsible for leptogenesis and have shown that these phases also have correlations with low energy CP violating phases., Comment: 35 pages, 16 figures, discussion and reference added, version to appear in Phys. Rev. D

To understand the mass spectra of charged lepton and neutrino $A_4$ symmetry has been proposed in addition with the Standard $SU(2)_L\times U(1)_Y$ model. We break $A_4$ symmetry softly and the deviation from the tri-bimaximal mixing arises due to Zee mechanism. In the present work, we express two mixing angles $\theta_{13}$ and $\theta_{23}$ in terms of a single model parameter and experimental observables, such as, mixing angle $\theta_{12}$, mass squared differences $\Delta m^2_{21}$ and $\Delta m^2_{32}$. Using the experimental values of $\theta_{23}$, $\theta_{12}$, $\Delta m^2_{21}$ and $\Delta m^2_{32}$ we restrict the model parameter and we predict $\theta_{13}$. This model gives rise to $\theta_{13}\simeq 11^\circ$ if we allow $1\sigma$ deviation of $\theta_{23}$ and $2^\circ$ deviation of $\theta_{12}$ from their best fit values. Utilizing all those constraints, we explore the extent of CP violation parameter $J_{\rm CP}$ in the present model and found a value of $J_{\rm CP}\approx 2.65\times 10^{-3}$ (for $1\sigma$ deviation of $\theta_{23}$ and $2^\circ$ deviation of $\theta_{12}$) consistent with the other neutrino experimental results. We have studied the mass pattern of neutrino and neutrinoless double beta decay $(\beta\beta_{0\nu})$ parameter $|(M_\nu)_{ee}|$ in this model., Comment: 16 pages, 6 eps figures,revised materials and figures, version to appear in Phys.Rev. D

Continuous $U(1)_{L_\mu-L_\tau}$ symmetry can generate quasi degenerate mass spectrum for both left handed light and right handed heavy Majorana neutrinos assuming that the symmetry preserving non zero parameters are nearly same. There is an accidental $\mu\tau$ exchange symmetry in the light and heavy neutrino Majorana mass terms. This implies $\theta_{13}=0$ and $\theta_{23}=\frac{\pi}{4}$. In addition it generates another zero mixing angle and one zero mass difference. We restrict ourselves to type-I See-Saw mechanism for generation of light neutrino mass. We have found that under $U(1)_{L_\mu-L_\tau}$ symmetry cosmological lepton asymmetry vanishes. We break $U(1)_{L_\mu-L_\tau}$ such a way that the $\mu\tau$ exchange symmetry preserves in the neutrino sector. We have seen that light neutrino phenomenology can be explained under soft breaking of this symmetry. We have observed that softness of this symmetry breaking depends on the degeneracy of the light neutrino mass spectrum. Quasi-degeneracy of right handed neutrino mass spectrum opens an option for resonant leptogenesis. The degeneracy of the right handed neutrino mass spectrum is restricted through light neutrino data. We observed that for generation of right sized baryon asymmetry common neutrino mass scale $m_0$ have to be of the order of $\sqrt{\Delta m^2_{\rm atm}}$ and corresponding right handed neutrino mass scale have to be nearly $10^{13}$ GeV. We also have discussed the effect of RG evolution on light neutrino spectrum and also on baryon asymmetry., Comment: 21 pages, no figure, Revised with the comments on RG effect

We show that a modification of a recently proposed model by Altarelli and Feruglio with softly broken $A_4$ symmetry leads naturally to nonvanishing $U_{e3}$ with $\theta_{13}\simeq 2^o - 4^o$. The observed mass squared differences for solar and atmospheric neutrinos have been fitted without fine tuning among model parameters. The predicted solar neutrino mixing angle is brought down from the tri-bimaximal prediction to be in concordance with the latest global analysis including experimental data from KamLAND and SNO., Comment: 10 Pages, 1 figure, reference added, few changes in text

We calculate the physical scalar contribution to the fermionic self energy matrix at one loop. We make a comment about the difference of our results from those in the existing literature., Comment: 4 pages, no figures

We work in a model where all CP violating phenomena have a common source. CP is spontaneously broken at a large scale $V$ through the phase of a complex singlet scalar. An additional $SU(2)_L$ singlet vector-like down-type quark relates this high scale CP violation to low energy. We quantitatively analyze this model in the quark sector. We obtain the numerical values of the parameters of the Lagrangian in the quark sector for a specific ansatz of the $4\times4$ down-type quark mass matrix where the weak phase is generated minimally. $Z \bar b b$ vertex will modify in presence of the extra vector-like down-type quark. From the experimental lower bound of the partial decay width $Z\to \bar b b$ we find out the lower bound of the additional down-type quark mass. Tree level flavor changing neutral current appears in this model due to the presence of the extra vector-like down-type quark. We give the range of values of the mass splitting $\Delta m_{B_q}$ in $B^0_q-{\bar B}^0_q$ system using SM box, $Z$ mediating tree level and $Z$ mediating one loop diagrams together for both $q=d, s$. We find out the analytical expression for $\Gamma_{12}^q$ in this model from standard box, $Z$ and Higgs mediated penguin diagrams for $B^0_q-{\bar B}^0_q$ system, $q=d,s$. From this we numerically evaluate the decay width difference $|\Delta\Gamma_{B_q}/\Gamma_{B_q}|$. We also find out the numerical values of the CP asymmetry parameters $a_J$ and $a_\pi$ for the decays $B^0_d\to J/\psi K_s$ and $B^0_d\to \pi^+ \pi^-$ respectively. We get the lower bound of the scale $V$ through the upper bound of the strong CP phase., Comment: 20 pages, no figures New materials and references have been added. Text has been modified. To be appear in J.Phys. G