In this paper, we consider a set of new symmetries in the SM, {\it diagonal reflection} symmetries $R \, m_{u,ν}^{*} \, R = m_{u,ν}, ~ m_{d,e}^{*} = m_{d,e}$ with $R =$ diag $(-1,1,1)$. These generalized $CP$ symmetries predict the Majorana phases to be $α_{2,3} /2 \sim
0$ or $π/2$.
A realization of reflection symmetries suggests a broken chiral $U(1)_{\rm PQ}$ symmetry and a flavored axion. The axion scale is suggested to be $\langle θ_{u,d} \rangle \sim Λ_{\rm GUT} \, \sqrt{m_{u,d} \, m_{c,s}} / v \sim 10^{12} \, $[GeV].
By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase $δ_{CP} \simeq 203^{\circ},$ and $|m_{1}| \simeq 2.5$ or $6.2 \, $[meV].
In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix $Y_ν$ completely determine the structure of right-handed neutrino mass $M_{R}$. An $u-ν$ unification predicts mass eigenvalues to be $ (M_{R1} \, , M_{R2} \, , M_{R3}) = (O (10^{5}) \, , O (10^{9}) \, , O (10^{14})) \, $[GeV].
In this letter, we consider exact $μ-τ$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f = u,d,e$ and a symmetric matrix for neutrinos $ν_{L}$. By a bi-maximal transformation, all the mass matrices lead to $μ-τ$ reflection symmetric forms, which seperately satisfy $T_{u} \, m_{u,ν}^{*} \, T_{u} = m_{u,ν}$ and $T_{d} \, m_{d,e}^{*} \, T_{d} = m_{d,e}$. Reconciliation between the $μ-τ$ reflection symmetries and observed $\sin θ_{13}$ predicts $δ_{CP} \simeq 203^{\circ}$. Moreover, imposition of universal texture $(m_…
In this paper, we consider a three-zero texture with diagonal reflection symmetries in the SM. The three-zero texture has two less assumptions ($(M_{u})_{11} , (M_ν)_{11} \neq 0$) than the universal four-zero texture of mass matrices $(M_{f})_{11} = (M_{f})_{13,31} = 0$ for $f = u,d,ν, e$. The texture allows diagonal reflection symmetries to be almost exact and $d$\,-\,$e$ unification. They reproduce the CKM and MNS matrices with accuracies of $O(10^{-4})$ and $O(10^{-3})$. Some perturbative diagonalizations yield two relations with good accuracy for quark mass and mixing. Although this calcul…
In view of the recent measurement of nonzero $θ_{13}$, we carry out a systematic study of a simple class of neutrino models that has one diagonal texture or cofactor zero in the mass matrix. There are seven free parameters in the model and five of them are already measured by neutrino oscillation experiments; some cases for the normal or inverted hierarchy are excluded and for the rest we obtain the preferred values for the lightest neutrino mass and Dirac CP phase. We find that there are strong similarities between one diagonal texture zero models with one mass hierarchy and one diagonal cofa…
In this paper, we impose a magic symmetry on the neutrino mass matrix $m_ν$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Δm_{i1}^{2}$, and the mixing angle $θ_{23}$. This scheme predicts $\sin θ_{13} = 0.149$, that is almost equal to the latest best fit, as a function of the lepton masses $m_{e, μ}$ and the mass differen…
The $μτ$-reflection symmetry is a simple symmetry capable of predicting all the unknown CP phases of the lepton sector and the atmospheric angle but too simple to predict the absolute neutrino mass scale or the mass ordering. We show that by combining it with a discrete abelian symmetry in a nontrivial way we can additionally enforce a texture-zero and obtain a highly predictive scenario where the lightest neutrino mass is fixed to be in the few meV range for two normal ordering (NO) solutions or in the tens of meV in one inverted ordering (IO) solution. The rate for neutrinoless double beta d…
Assuming that the neutrino mass matrix is diagonalized by the TBM, we looked for the charged lepton mass matrix textures which render a lepton mixing matrix consistent with data. We were interested in the textures with the maximum number of zeros, so, we explored the cases of real matrices with three (and also four zeros) and found which of them provide solutions in agreement with data. We present the successful Yukawa textures and obtained the relative sizes of their non-zero entries. We found some interesting relations among the entries of these textures in terms of the charged lepton masses…
The $μτ$-reflection symmetric neutrino mass matrix can accommodate all known neutrino mixing angles, with maximal atmospheric angle fixed, and predicts all the unknown CP phases of the lepton sector but is unable to predict the absolute neutrino mass scale. Here we present a highly predictive scenario where $μτ$-reflection is combined with a discrete abelian symmetry to enforce a texture-zero in the mass matrix of the heavy right-handed neutrinos that generate the light neutrino masses. Such a restriction reduces the free parameters of the low energy theory to zero and the absolute neutrino ma…
We investigate the texture structures of lepton mass matrices with four (five) non-zero elements in the charged lepton mass matrix and three (four) vanishing cofactors in the neutrino mass matrix. Using weak basis transformations, all possible textures for three and four vanishing cofactors in $M_ν$ are grouped into 7 classes and predictions for the unknown parameters such as the Dirac CP violating phase and the effective Majorana mass for the phenomenologically allowed textures have been obtained. We, also, illustrate how such texture structures can be realized using discrete Abelian flavor s…
Assuming a diagonal Majorana neutrino mass matrix, we investigate the neutrino Yukawa textures which lead to a non-zero reactor mixing angle $θ_{13}$. The neutrino effective coupling matrix $κ^{eff}$ is pre-diagonalized by a constant mixing pattern $V_ν$ with a vanishing $θ^ν_{13}$. The resulting pre-diagonal symmetrical matrix $κ$ is set to be four texture zeros with two types of off-diagonal elements nonzero, which is $κ_{13}$ and $κ_{23}$, respectively. With the expectation of simple textures we thoroughly classify the linear combinations, $α_{i}$, $β_{i}$ and $γ_{i}$ of Yukawa elements $λ_…
Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting rela…
In an attempt to find minimal scenarios we study the implications of Dirac and Majorana mass matrices with texture zeros within the type I seesaw mechanism. For the Dirac mass matrices we consider 5 zero textures which we show to be the most minimal form that can successfully account for low energy phenomenology if the Majorana mass matrices are chosen minimal as well. For those, we consider both diagonal and even more minimal non-diagonal forms. The latter can be motivated e.g. by simple U(1) flavour symmetries and have two degenerate eigenvalues. We classify the allowed textures and discuss …
Lepton mass matrices similar to texture 4 zero quark mass matrices, known to be quite successful in explaining the CKM phenomenology, have been considered for finding the mixing matrix element U_{e3} (\equiv s_{13}) respecting the CHOOZ constraint, with s_{12} and Δm_{12}^2 constrained by SNP and s_{23} and Δm_{23}^2 constrained by ANP. Taking charged lepton mass matrix M_l to be diagonal, we find that the ranges of s_{13} corresponding to different SNP solutions very well include the corresponding values of s_{13} found by Akhmedov et al. by considering neutrino mass matrix M_ν with no textur…
We discuss flavor-violating constraints and consequently possible charged Higgs boson phenomenology emerging from a four-zero Yukawa texture embedded within the Type-III 2-Higgs Doublet Model (2HDM-III). Firstly, we show in detail how we can obtain several kinds of 2HDMs when some parameters in the Yukawa texture are absent. Secondly, we present a comprehensive study of the main B-physics constraints on such parameters induced by flavor-changing processes, in particular on the off-diagonal terms of such a texture: i.e., from $μ-e$ universality in $τ$ decays, several leptonic B-decays ($B \to τ…
We study a variety of different texture patterns in the basis in which the charged lepton mass matrix or neutrino mass matrix or neither are diagonal. The experimental results on the neutrinos provide sufficient restrictions to allow only a small number of simple patterns. We discuss particularly the texture zeroes which provide important relations among the mass eigenvalues and the mixing matrix.
We study all possible texture zeros in the Majorana neutrino mass matrix which are allowed from neutrino oscillation as well as cosmology data when the charged lepton mass matrix is assumed to take the diagonal form. In case of one-zero texture, we write down the Majorana phases which are assumed to be equal and the lightest neutrino mass as a function of the Dirac CP phase. In case of two-zero texture, we numerically evaluate all the three CP phases and lightest neutrino mass by solving four real constraint equations. We then constrain texture zero mass matrices from the requirement of produc…
I systematically consider, in the context of the type-I see-saw mechanism, all the predictive cases in which both the Dirac mass matrix connecting the left-handed neutrinos to the right-handed neutrinos, and the Majorana mass matrix of the latter neutrinos, feature texture zeros, while the mass matrix of the charged leptons is diagonal. I have found a few cases which had not been discussed in the literature previously.
We study the origin of neutrino masses and mixing angles which can accomodate the LMA MSW solutions of the solar neutrino anomaly as well as the solution of the atmospheric neutrino problem, within the framework of the see-saw mechanism. We employ the diagonal form of the Dirac neutrino mass matrices with the physical masses as diagonal elements in the hierarchical order. Such choice has been motivated from the fact that the known CKM angles for the quark sector, are relatively small. We consider both possibilities where the Dirac neutrino mass matrix is either the charged lepton or the up-qua…
In this paper, we derive in a novel approach the possible textures of neutrino mass matrix that can lead us to maximal atmospheric mixing angle and Dirac CP phase which are consistent with the current neutrino oscillation data. A total of eleven textures are thus found. Interestingly, the specific texture given by the $μ$-$τ$ reflection symmetry can be reproduced from one of the obtained textures. For these textures, some neutrino mass sum rules which relate the neutrino masses and Majorana CP phases will emerge.
We present the generic formulas to calculate the ratios of neutrino masses and the Majorana phases of CP violation from the neutrino mass matrix with two independent vanishing entries in the flavor basis where the charged lepton mass matrix is diagonal. An order-of-magnitude illustration is given for seven experimentally acceptable textures of the neutrino mass matrix, and some analytical approximations are made for their phenomenological consequences at low energy scales.
We respond to the comments of S. Sharma et al. [Phys. Rev. D 91, 038301 (2015)] on my recent paper, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)]. In their comments, they begin discussing a particular class of five-zero texture non-Fritzsch-like quark mass matrix, which was proposed by me, and questioning its validity. Then, they put in doubt the phases included in the unitary matrices used for diagonalizing the quark mass matrices, from which they claim that the CP violating parameter $ε_k$ obtained does not agree with the experimental value. Because of these comments, finally, they recommend b…
We construct the CP-odd weak basis invariants from the neutrino mass matrix in a weak basis in which the charged lepton mass matrix is diagonal and find the necessary and sufficient conditions for CP conservation. We study the interrelationships between different CP-odd weak basis invariants to examine their implications for the Dirac and Majorana type CP violating phases for the phenomenologically allowed Frampton-Glashow-Marfatia texture zero structures of the neutrino mass matrix.
In an attempt at explaining the observed neutrino mass-squared differences and leptonic mixing, lepton mass matrices with zero textures have been widely studied. In the weak basis where the charged lepton mass matrix is diagonal, various neutrino mass matrices with two zeros have been shown to be consistent with the current experimental data. Using the canonical and Smith normal form methods, we construct the minimal Abelian symmetry realizations of these phenomenological two-zero neutrino textures. The implementation of these symmetries in the context of the seesaw mechanism for Majorana neut…
We systematically analyze the Dirac and the Majorana mass matrices in seesaw models with two heavy right-handed neutrinos. We perform thorough classification of the vanishing matrix elements which are compatible with the results from the current neutrino oscillation experiments. We include the possibility of a non-diagonal Majorana mass matrix which leads to new solutions viable with data. In a basis where the Majorana mass matrix is diagonal, these solutions imply a Dirac matrix with specific relationships amongst its elements. We find that at the level of total 4 zeros together in the Dirac …
The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U- and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approximation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangular form. This parameterization could serve as a useful starting point for model building. Examples of mass textures are analyzed using this method.
We perform a systematic study of neutrino mass matrices having a vanishing cofactor and an equality between two cofactors of the mass matrix. Such texture structures of the effective neutrino mass matrix arise from type-I seesaw mechanism when the Dirac neutrino mass matrix is diagonal with equal elements and the right-handed Majorana neutrino mass matrix has hybrid textures with one equality of matrix elements and one zero matrix element. For three right-handed neutrinos there are sixty possible hybrid textures out of which only six are excluded by the present experimental data. We show that …
Within the type-I seesaw and in the basis where charged lepton and heavy neutrino mass matrices are real and diagonal, $μτ$ symmetric four and three zero neutrino Yukawa textures are perturbed by lowest order $μτ$ 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 $θ_{13}$ in the observed range, provided all the …
We propose a new texture for the light neutrino mass matrix. The proposal is based upon imposing zero-trace condition on the two by two sub-matrices of the complex symmetric Majorana mass matrix in the flavor basis where the charged lepton mass matrix is diagonal. Restricting the mass matrix to have two traceless sub-matrices may be found sufficient to describe the current data. Eight out of fifteen independent possible cases are found to be compatible with current data. Numerical and some approximate analytical results are presented.
We study the possibility of probing different texture zero neutrino mass matrices at long baseline neutrino experiment DUNE. Assuming a diagonal charged lepton basis and Majorana nature of light neutrinos, we first classify the possible light neutrino mass matrices with one and two texture zeros and then numerically evaluate the parameter space in terms of atmospheric mixing angle $θ_{23}$ and Dirac CP phase $δ_{\text{CP}}$ which satisfies the texture zero conditions. We then feed these parameter values into the numerical analysis in order to study the sensitivity of DUNE experiment to them. W…
In the light of latest neutrino oscillation data, we have investigated the one zero Majorana neutrino mass matrix $M_ν$ with zero sum condition of mass eigen values in the flavor basis, where charged lepton mass matrix is diagonal. Among the six possible one-zero cases, it is found that only five can survive the current experimental data, while case with (1, 1) vanishing element of $M_ν$ is ruled out, if zero trace condition is imposed at 3$σ$ confidence level (CL). Numerical and some approximate analytical results are presented.
We classify all possible texture zeros in light neutrino mass matrix in diagonal charged lepton basis by considering Dirac nature of light neutrinos. For Hermitian nature of neutrino mass matrix, the number of possible texture zeros remain same as Majorana texture zeros, but with less free parameters due to the absence of additional Majorana CP phases. Relaxing the Hermitian nature of neutrino mass matrix lead to many more possibilities and freedom due to additional CP phases, mixing angles not constrained by neutrino data. While we find that none of the texture zeros in Hermitian case are all…
Following the Occam's razor principle, we explore the particular textures (featuring texture zeros and equalities) of the Dirac neutrino mass matrix in the minimal seesaw model (where only two right-handed neutrinos $N^{}_1$ and $N^{}_2$ are responsible for the generation of the light neutrino masses), in light of current neutrino experimental results and leptogenesis. The study will be performed for two particular patterns of the Majorana mass matrix $M^{}_{\rm R}$ for $N^{}_1$ and $N^{}_2$: (A) $M^{}_{\rm R}$ being diagonal $ \left( \begin{array}{cc} M^{}_1 & 0 \cr 0 & M^{}_2 \cr \end{array}…
The recent enormous improvement of our knowledge of the neutrino oscillation parameters has motivated us to reinvestigate the allowed ranges of the elements of the neutrino mass matrix in the basis where the charged-lepton mass mass matrix is diagonal. Moreover, we have studied the correlations of the elements of the neutrino mass matrix. The result of this analysis is useful for finding textures in the neutrino mass matrix and, therefore, for model building in the lepton sector. As an example, we present two textures of the neutrino mass matrix which have only two parameters and fit very well…
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…
We study the existence of one/two texture zeros or one/two vanishing minors in the neutrino mass matrix with $μτ$ symmetry. In the basis where the charged lepton mass matrix and the Dirac neutrino mass matrix are diagonal, the one/two zeros or one/two vanishing minors in the right-handed Majorana mass matrix having $μτ$ symmetry will propagate via seesaw mechanism as one/two vanishing minors or one/two texture zeros in the neutrino mass matrix with $μτ$ symmetry respectively. It is found that only five such texture structures of the neutrino mass matrix are phenomenologically viable. For tribi…
The Two Higgs Doublets Model (2HDM) has provided a very useful way to describe a minimal extension of the scalar sector of the Standard Model. In this work, it is shown a scheme that we call Partial Aligned Two Higgs Doublet Model (PA-2HDM) which allows a description of the distinct versions of the 2HDM in a simple way, including those with flavor symmetries. In addition, it is shown a method to diagonalize Yukawa matrices of four-zero texture coming from the 2HDM-III. We provide some phenomenological applications in order to show the model's predictive power.
Here we show that the Weak Basis Transformation is an appropriate mathematical tool that can be used to find texture zeros in the quark mass matrix sector of the Standard Model. So, starting with the most general quark mass matrices and taking physical data into consideration, is possible to obtain more than three texture zeros by any weak basis transformation. Where the most general quark mass matrices considered in the model, were obtained through a special weak basis wherein the mass matrix $M_u$~(or $M_d$) has been taken to be diagonal and only the matrix $M_d$~(or $M_u$) is considered to …
Starting from a weak basis in which the up (or down) quark matrix is diagonal, we obtain an exact set of equations for the quark mass matrix elements in terms of known observables. We make a numerical analysis of the down (up) quark mass matrix. Using the data available for the quark masses and mixing angles at different energy scales, we found a numerical expression for these matrices. We suggest that it is not possible to have an specific texture from this analysis. We also examine the most general case when the complex phases are introduced in the mass matrix. We find the numerical value fo…
We consider a restricted Type-I seesaw scenario with four texture zeros in the neutrino Yukawa matrix, in the weak basis where both the charged-lepton Yukawa matrix and the Majorana mass matrix for right-handed neutrinos are diagonal and real. Inspired by grand unified theories, we further require the neutrino Yukawa matrix to exhibit a similar hierarchical pattern to that in the up-type quark Yukawa matrix. With such a hierarchy requirement, we find that leptogenesis, which would operate in a $N_2^{}$-dominated scenario with the asymmetry generated by the next-to-lightest right-handed neutrin…
An ansatz for mass matrix was recently proposed for charged leptons, predicting (in its diagonal approximation) $m_τ\simeq1776.80$ MeV from the experimental values of $m_e$ and $m_μ$, in agreement with $m_τ^{exp}= 1777.00^{+0.30}_{-0.27}$ MeV. Now it is applied to neutrinos. If the amplitude of neutrino oscillations $ν_μ\toν_τ$ is $\sim 1/2$ and $|m^2_{ν_τ}-m^2_{ν_μ}|\sim(0.0003 to 0.01) eV^2$, as seems to follow from atmospheric-neutrino experiments, this ansatz predicts $m_{ν_e}\ll m_{ν_μ}\sim(0.2 to 1)\times 10^{-2} $ eV and $m_{ν_τ}\sim(0.2 to 1)\times 10^{-1} eV$, and also the amplitude o…
Quark-lepton symmetry has been shown to be inconsistent with baryogenesis via leptogenesis in natural schemes of the see-saw mechanism. Within the phenomenological approach of textures, we relax this strict symmetry and propose weaker conditions, namely models of the neutrino Dirac mass matrix $M_D$ which have the same hierarchy as the matrix elements of $M_u$. We call this guide-line generalized $hierarchical$ quark-lepton symmetry. We consider in detail particular cases in which the moduli of the matrix elements of $M_D$ are equal to those of $M_u$. Within the phenomenological approach of te…
We classify the textures of the Dirac and the right-handed Majorana neutrino mass matrices, $M_D$ and $M_R$, which can satisfy the so-called ``Strong Scaling Ansatz'' (SSA) within the framework of the seesaw mechanism $M_ν=-M_D^T M_R^{-1} M_D$. We assume that the Dirac neutrino mass matrix has some texture zeros and examine which elements should be zero in order to satisfy the SSA, by taking into account all possible textures for $M_R$. We find that the resulting Dirac neutrino mass matrices have rank 2 as well as the rank of the effective neutrino mass matrix $M_ν$, or rank 1, depending only …
An explicit form of charged--lepton mass matrix, predicting $ m_τ= 1776.80 $~MeV from the experimental values of $ m_e $ and $ m_μ$ (in good agreement with the experimental figure $ m_τ= 1777.05^{+0.29}_{-0.26}$ MeV), is applied to three neutrinos $ν_e $, $ν_μ$, $ν_τ$ in order to correlate tentatively their masses and mixing parameters. While for charged leptons the off--diagonal mass--matrix elements turn out to be small {\it versus} its diagonal elements, it is suggested that for neutrinos the situation is inverse. Under such a conjecture, the neutrino masses, lepton \CKM matrix and neutrino…
A new explicit model of neutrino texture is presented, where in the overall 6x6 mass matrix the lefthanded and righthanded Majorana 3x3 components are diagonal with equal entries of opposite sign, while the Dirac 3x3 component is given as a diagonal hierarchical structure (possibly similar to the charged lepton and quark 3x3 mass matrices) deformed by the popular nearly bimaximal 3x3 mixing matrix. Then, all neutrino masses are light and m_1 = -m_4, m_2 = -m_5, m_3 = -m_6. The resulting neutrino oscillation formulae are identical with those working in the effective texture of three active neut…
We study the zero textures of the Yukawa matrices in the minimal extended type-I seesaw (MES) model which can give rise to $\sim$ eV scale sterile neutrinos. In this model, three right handed neutrinos and one extra singlet $S$ are added to generate a light sterile neutrino. The light neutrino mass matrix for the active neutrinos, $ m_ν$, depends on the Dirac neutrino mass matrix ($ M_{D} $), Majorana neutrino mass matrix ($ M_{R} $) and the mass matrix ($ M_{S} $) coupling the right handed neutrinos and the singlet. The model predicts one of the light neutrino masses to vanish. We systematica…
In the light of several recent analyses pointing towards texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized 'u-diagonal' basis within the Standard Model framework using the Unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured 1$σ$ values of the three physical parameters namely $m_{\rm{u}}$, $m_{\rm{d}}$ and $s_{12}$…
It is well-known that, in the basis where the charged-lepton mass matrix is diagonal, there are seven cases of two texture zeros in Majorana neutrino mass matrices that are compatible with all experimental data. We show that two of these cases, namely B3 and B4 in the classification of Frampton, Glashow and Marfatia, are special in the sense that they automatically lead to near-maximal atmospheric neutrino mixing in the limit of a quasi-degenerate neutrino mass spectrum. This property holds true irrespective of the values of the solar and reactor mixing angles because, for these two cases, in …
An attempt is made to generate the bimaximal mixings of the three species of neutrinos from the textures of the right-handed Majorana neutrino mass matrices. We extend our earlier work in this paper for the generation of the nearly degenerate as well as the inverted hierarchical models of the left-handed Majorana neutrino mass matrices using the non-diagonal textures of the right-handed Majorana neutrino mass matrices and the diagonal form of the Dirac neutrino mass matrices, within the frame work of the seesaw mechanism in a model independent way. Such Majorana neutrino mass models are import…
We construct a new set of combinations from the mass matrices of the charged leptons and neutrinos that are invariant under basis transformation, hereafter {\it the} invariants. We use these invariants to study various symmetries and neutrino mass textures in a basis independent way. In particular, we show that by using these invariants the ansatz such as $μ-τ$ exchange and reflection symmetries, various texture zeros and flavor symmetries can be expressed in a general basis.
We study all possible neutrino mass matrices with one zero element and two equal non-zero elements, known as hybrid texture neutrino mass matrices. In the diagonal charged lepton basis, we consider thirty nine such possible cases which are consistent with the latest neutrino data. Using the two constraints on neutrino mass matrix elements imposed by hybrid textures, we numerically evaluate the neutrino parameters like the lightest neutrino mass $m_{\text{lightest}}$, one Dirac CP phase $δ$ and two Majorana CP phases $α, β$ by using the global fit $3σ$ values of three mixing angles and two mass…
Applying the $A_4$ symmetry in the scenario of unimodular second scheme of trimaximal $TM_2$ mixing matrix, where the charged lepton mass matrix is diagonal and the nature of neutrinos are Majorana, we investigate and analyze feasible two zeros neutrino mass matrices. Among the seven possible two-zero textures with $A_4$ symmetry, we have found that only two textures, namely the texture with $(e, e)$ and $(e,μ)$ vanishing element of mass matrix and its permutation, are consistent with the experimental data in the non-perturbation method. We also obtain new significant relations between phases …
We present predictions for CP violating phases of the Type-I seesaw model with four-zero textures on the Dirac mass matrix. For the four-zero textures, the effective low energy Majorana mass matrix is parametrized with seven parameters. They are three mass-dimensional parameters, two angles and two CP violating sources. The number of these parameters is less than that of the general description of the Majorana mass matrix with three neutrino masses, three mixing angles and three CP violating phases. In particular, only two independent CP violating sources give rise to three CP violating phases…
We construct a texture where the Seesaw matrix is diagonalized by the TriBiMaximal (TBM) matrix with a phase. All CKM and PMNS angles are within their pdg values, and the mass relations of quarks and charged leptons extrapolated to GUT scale are satisfied, including the Gatto relation. The novel ingredient is the asymmetry of the down-quark and charged lepton Yukawa matrices. Explaining the reactor angle requires a $\require{cancel} \cancel {CP}$ phase in the TBM matrix, resulting in the Jarlskog-Greenberg invariant at $|J|=0.028$, albeit with an undetermined sign. While $SO(10)$ restrains the…
