Lepton Mass Matrices Research Articles

Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw

In the framework of the two right-handed neutrino seesaw model, we consider maximally-restrictive texture-zero patterns for the lepton Yukawa coupling and mass matrices, together with the existence of a remnant CP symmetry. Under this premise, we find that several textures are compatible with the most recent data coming from neutrino oscillation and neutrinoless double beta decay experiments. It is shown that, the maximum number of allowed texture zeros in the Dirac Yukawa coupling matrix is two, for an inverted neutrino mass spectrum. In contrast, for Yukawa coupling matrices with just one texture zero, both normal and inverted orderings of neutrino masses are compatible with data. In all cases, the predictions for the low-energy Dirac and Majorana CP-violating phases, and for the effective mass parameter relevant in neutrinoless double-beta decay experiments, are presented and discussed. We also comment on the impact of future experimental improvements in scrutinising texture-zero patterns with a remnant CP symmetry, within the minimal version of the seesaw mechanism considered here.

Texture zero mass matrices and nature of neutrinos

For Majorana as well as Dirac neutrinos, attempt has been made to carry out a comparative study of the predictions of Fritzsch-like texture 6, 5 and 4 zero leptonic mass matrices. In particular, considering normal hierarchy of neutrino masses, we have examined how the parameter space available to the mixing angles with respect to the lightest neutrino mass changes for the two types of neutrinos.

Modular A4 invariance and neutrino mixing

We study the phenomenological implications of the modular symmetry Γ(3) ≃ A4 of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus τ, which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with A4 symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted sin2θ23 is restricted to be larger than 0.54 and δCP = ±(50°-180°). Since the correlation of sin2θ23 and δCP is sharp, the prediction is testable in the future. It is remarkable that the effective mass mee of the neutrinoless double beta decay is around 22 meV while the sum of neutrino masses is predicted to be 145 meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.

Neutrino predictions from generalized CP symmetries of charged leptons

We study the implications of generalized CP transformations acting on the mass matrices of charged leptons in a model-independent way. Generalized e − μ, e − τ and μ−τ symmetries are considered in detail. In all cases the physical parameters of the lepton mixing matrix, three mixing angles and three CP phases can be expressed in terms of a restricted set of independent “theory parameters” that characterize a given choice of CP transformation. This leads to implications for neutrino oscillations as well as neutrinoless double beta decay experiments.

Minimal type-I seesaw model with maximally restricted texture zeros

In the context of Standard Model (SM) extensions, the seesaw mechanism provides the most natural explanation for the smallness of neutrino masses. In this work we consider the most economical type-I seesaw realization in which two right-handed neutrinos are added to the SM field content. For the sake of predictability, we impose the maximum number of texture zeros in the lepton Yukawa and mass matrices. All possible patterns are analyzed in the light of the most recent neutrino oscillation data, and predictions for leptonic $CP$ violation are presented. We conclude that, in the charged-lepton mass basis, eight different texture combinations are compatible with neutrino data at $1\ensuremath{\sigma}$, all of them for an inverted-hierarchical neutrino mass spectrum. Four of these cases predict a $CP$-violating Dirac phase close to $3\ensuremath{\pi}/2$, which is around the current best-fit value from the global analysis of neutrino oscillation data. If one further reduces the number of free parameters by considering three equal elements in the Dirac neutrino Yukawa coupling matrix, several texture combinations are still compatible with data but only at $3\ensuremath{\sigma}$. For all viable textures, the baryon asymmetry of the Universe is computed in the context of thermal leptogenesis, assuming (mildly) hierarchical heavy Majorana neutrino masses ${M}_{1,2}$. It is shown that the flavored regime is ruled out, while the unflavored one requires ${M}_{1}\ensuremath{\sim}{10}^{14}\text{ }\text{ }\mathrm{GeV}$.

Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?

We provide a complete answer to the following question: what are the flavour groups and representations providing, in the symmetric limit, an approximate description of lepton masses and mixings? We assume that neutrino masses are described by the Weinberg operator. We show that the pattern of lepton masses and mixings only depends on the dimension, type (real, pseudoreal, complex), and equivalence of the irreducible components of the flavour representation, and we find only six viable cases. In all cases the neutrinos are either anarchical or have an inverted hierarchical spectrum. In the context of SU(5) unification, only the anarchical option is allowed. Therefore, if the hint of a normal hierarchical spectrum were confirmed, we would conclude (under the above assumption) that symmetry breaking effects must play a leading order role in the understanding of neutrino flavour observables. In order to obtain the above results, we develop a simple algorithm to determine the form of the lepton masses and mixings directly from the structure of the decomposition of the flavour representation in irreducible components, without the need to specify the form of the lepton mass matrices.

The Texture One-Zero Neutrino Mass Matrix with Vanishing Trace

In the light of latest neutrino oscillation data, we have investigated the one-zero Majorana neutrino mass matrix Mν with zero sum condition of mass eigenvalues 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 Mν is ruled out, if zero trace condition is imposed at 3σ confidence level (CL). Numerical and some approximate analytical results are presented.

The neutrino flavor puzzle

The neutrino flavor puzzle

Neutrino mass matrices with three or four vanishing cofactors and nondiagonal charged lepton sector

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 $M_{\nu}$ 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 symmetries.

Towards the minimal seesaw model via CP violation of neutrinos

We study the minimal seesaw model, where two right-handed Majorana neutrinos are introduced, focusing on the CP violating phase. In addition, we take the trimaximal mixing pattern for the neutrino flavor where the charged lepton mass matrix is diagonal. Owing to this symmetric framework, the 3 × 2 Dirac neutrino mass matrix is given in terms of a few parameters. It is found that the observation of the CP violating phase determines the flavor structure of the Dirac neutrino mass matrix in the minimal seesaw model. New minimal Dirac neutrino mass matrices are presented in the case of TM1, which is given by the additional 2-3 family mixing to the tri-bimaximal mixing basis in the normal hierarchy of neutrino masses. Our model includes the Littlest seesaw model by King et al. as one of the specific cases. Furthermore, it is remarked that our 3 × 2 Dirac neutrino mass matrix is reproduced by introducing gauge singlet flavons with the specific alignments of the VEV’s. These alignments are derived from the residual symmetry of S4 group.

On expansions in neutrino effective field theory

We match the seesaw model for generating neutrino masses onto the Standard Model Effective Field Theory (SMEFT). We perform this matching at tree level up to dimension seven in the operator expansion. We explain how some of the perturbations of the neutrino mass matrix due to operators of mass dimension greater than five are tied to integrating out the heavy Majorana mass eigenstates in sequence. We demonstrate that the low energy limit of seesaw models are well described by the SMEFT, particularly when constructed using a flavour space expansion. Flavour space expansions of seesaw models are of interest as the coupling of the heavy states to the Standard Model, that are integrated out to generate neutrino masses, are through flavour space vectors ∈ {mathbb{C}}^3 . We point out that neutrino phenomenology can be systematically developed as a perturbation around the unknown eigenvectors diagonalizing the charged lepton mass matrix using the fact that these eigenvectors also form a basis of {mathbb{C}}^3 . This point holds in seesaw models and can also be applied to other models of neutrino mass generation to develop systematic expansions. We develop the algebra for this flavour space and discuss some phenomenology to illustrate this approach.

A4 realization of the inverse seesaw mechanism: Neutrino masses, θ13 , and leptonic nonunitarity

We provide an $A_4$ based flavor symmetric scenario to accommodate the inverse seesaw mechanism for explaining light neutrino masses and mixing. We find that the lepton mixing, in particular the tri-bimaximal mixing pattern and its deviation through nonzero $\theta_{13}$, is originated solely from the flavor structure of the lepton number violating contribution of the neutral lepton mass matrix. Here we discuss in detail how a nonzero value of $\theta_{13}$ is correlated with the other parameters in the framework and its impact on the Dirac CP phase $\delta$. We also analyze the non-unitarity effects on lepton mixing matrix and its implication in terms of the lepton flavor violating decays, etc..

Common origin of nonzero θ13 and dark matter in an S4 flavor symmetric model with inverse seesaw mechanism

We study an inverse seesaw model of neutrino mass within the framework of $S_4$ flavour symmetry from the requirement of generating non-zero reactor mixing angle $\theta_{13}$ along with correct dark matter relic abundance. The leading order $S_4$ model gives rise to tri-bimaximal type leptonic mixing resulting in $\theta_{13}=0$. Non-zero $\theta_{13}$ is generated at one loop level by extending the model with additional scalar and fermion fields which take part in the loop correction. The particles going inside the loop are odd under an in-built $Z^{\text{Dark}}_2$ symmetry such that the lightest $Z^{\text{Dark}}_2$ odd particle can be a dark matter candidate. Correct neutrino and dark matter phenomenology can be achieved for such one loop corrections either to the light neutrino mass matrix or to the charged lepton mass matrix although the latter case is found to be more predictive. The predictions for neutrinoless double beta decay is also discussed and inverted hierarchy in the charged lepton correction case is found to be disfavoured by the latest KamLAND-Zen data.

Texture zero mass matrices and CP violation

Within the Standard Model, using the facility of making Weak Basis transformations, attempt has been made to examine the most general mass matrices within the texture zero approach. For the case of quarks, interestingly, one finds a particular set of texture four zero quark mass matrices emerging out to be a unique viable option for the description of quark mixing data as well as for accommodation of CP violation. Similarly, general lepton mass matrices, essentially considered as texture zero mass matrices, yield interesting bounds on the CP violating Jarlskog’s rephasing invariant parameter in the leptonic sector.

Flavon VEV scales in U(3)×U(3)′ model

We have recently proposed a quark and lepton mass matrix model based on U(3)[Formula: see text]×[Formula: see text]U(3)[Formula: see text] family symmetry as the so-called Yukawaon model, in which the U(3) symmetry is broken by VEVs of flavons [Formula: see text] which are [Formula: see text] of U(3)[Formula: see text]×[Formula: see text]U(3)[Formula: see text]. The model has successfully provided the unified description of quark and lepton masses and mixings by using the observed charged lepton masses as only family-number dependent input parameters. However, our final goal is not only to give well-satisfied fitting of quark and lepton masses and mixings, but also to investigate physics behind such a successful parameter fitting. Therefore, our next concern is scales of VEVs of the flavons because we have not paid attention to scales of flavons in the previous study. In order to give consistency among the scales, the previous flavon model is drastically changed together with economizing number of the flavons, but with keeping previous phenomenological success. We estimate that VEVs of flavons with [Formula: see text], [Formula: see text] and [Formula: see text] are of the orders of 10 TeV, 104 TeV and 107 TeV, respectively.

Electron and muon anomalous magnetic dipole moment in a 3\u20133\u20131 model

We calculate, in the context of a 3–3–1 model with heavy charged leptons, constraints on some parameters of the extra particles in the model by imposing that their contributions to both the electron and muon (g − 2) factors are in agreement with experimental data up to 1σ-3σ. In order to obtain realistic results we use some of the possible solutions of the left- and right-unitary matrices that diagonalize the lepton mass matrices, giving the observed lepton masses and at the same time allowing to accommodate the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix. We show that, at least up to 1-loop order, in the particular range of the space parameter that we have explored, it is not possible to fit the observed electron and muon (g − 2) factors at the same time unless one of the extra leptons has a mass of the order of 20–40 GeVs and the energy scale of the 331 symmetry to be of around 60–80 TeVs.

Flavor mixings in flux compactifications

A multiplicity of quark-lepton families can naturally arise as zero-modes in flux compactifications. The flavour structure of quark and lepton mass matrices is then determined by the wave function profiles of the zero-modes. We consider a supersymmetric $SO(10)\times U(1)$ model in six dimensions compactified on the orbifold $T^2/{\mathbb Z_2}$ with Abelian magnetic flux. A bulk $\mathbf{16}$-plet charged under the $U(1)$ provides the quark-lepton generations whereas two uncharged $\mathbf{10}$-plets yield two Higgs doublets. Bulk anomaly cancellation requires the presence of additional $\mathbf{16}$- and $\mathbf{10}$-plets. The corresponding zero-modes form vectorlike split multiplets that are needed to obtain a successful flavour phenomenology. We analyze the pattern of flavour mixings for the two heaviest families of the Standard Model and discuss possible generalizations to three and more generations.

Maximally restrictive leptonic texture zeros in two-Higgs-doublet models

The implementation of maximally restrictive texture zeros in the leptonic sector is investigated in the context of two-Higgs-doublet models with Majorana neutrinos. After analyzing all maximally restrictive pairs of leptonic mass matrices with zero entries, we conclude that there are only four texture combinations that are compatible with observations at 3σ confidence level and can be implemented through Abelian symmetries in a two-Higgs-doublet model. The compatibility of these textures with current constraints on lepton-flavor-violating processes is also studied. The ultraviolet completion of these models is discussed in the framework of the seesaw mechanism for neutrino masses.

Sparticle spectroscopy of the minimal SO(10) model

The supersymmetric (SUSY) minimal SO(10) model is a well-motivated grand unified theory, where the Standard Model (SM) fermions have Yukawa couplings with only one 10-plet and one 126‾-plet Higgs fields and it is highly non-trivial if the realistic quark and lepton mass matrices can be reproduced in this context. It has been known that the best fit for all the SM fermion mass matrices is achieved by a vacuum expectation value of the 126‾-plet Higgs field being at the intermediate scale of around O(1013) GeV. Under the presence of the SO(10) symmetry breaking at the intermediate scale, the successful SM gauge coupling unification is at risk and likely to be spoiled. Recently, it has been shown that the low-energy fermion mass matrices, except for the down-quark mass predicted to be too low, are very well-fitted without the intermediate scale. In order to resolve the too-low down quark mass while keeping the other fittings intact, we consider SUSY threshold corrections to reproduce the right down quark mass. It turns out that this requires flavor-dependent soft parameters. Motivated by this fact, we calculate particle mass spectra at low energies with flavor-dependent sfermion masses at the grand unification scale. We present a benchmark particle mass spectrum which satisfies a variety of phenomenological constraints, in particular, the observed SM-like Higgs boson mass of around 125 GeV and the relic abundance of the neutralino dark matter as well as the experimental result of the muon anomalous magnetic moment. In the resultant mass spectrum, sleptons in the first and second generations, bino and winos are all light, and this scenario can be tested at the LHC Run-2 in the near future.

Alternative schemes of predicting lepton mixing parameters from discrete flavor and CP symmetry

We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the residual groups of the structure $Z_2\times CP$ in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters $\theta_{\nu}$ and $\theta_{l}$. This type of breaking pattern is extended to the quark sector. In the second scheme, an abelian subgroup contained in the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant $CP$ transformation, all lepton mixing parameter are determined in terms of three free parameters $\theta_{1, 2, 3}$. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters $\theta_{\nu, l}$ and $\theta_{1, 2, 3}$ is taken into account. We have studied the lepton mixing patterns arising from the flavor group $S_4$ and $CP$ symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.