Charged Lepton Mass Matrix Research Articles

Orbifold modular GUT of flavor

We discuss an SU(5) grand unified theory based on the 10d orbifold (T2)3/(Z4×Z2) plus three modular S4 groups with moduli at respective fixed points i,i+2,ω=e2iπ/3. The resulting model has hierarchical quark and charged-lepton mass matrices, arising from a double weighton mechanism, and reproduces the highly predictive littlest seesaw mechanism in the neutrino sector. The down-quark mass matrix has an upper triangular form, contributing to Cabibbo-Kobayashi-Maskawa mixing, while the charged-lepton mass matrix has a lower-triangular form with suppressed contributions to Pontecorvo-Maki-Nakagawa-Sakata mixing. The orbifold yields successful SU(5) breaking with doublet-triplet splitting of the Higgs multiplets. Published by the American Physical Society 2024

Neutrino mixing matrix and masses from a particular two-zero texture based on A 4 symmetry

The current study aims to investigate the particular case of two zeros in a Majorana neutrino mass matrix based on A 4 symmetry, where charged lepton mass matrix is diagonal. The texture is with (μ, μ) and (τ, τ) vanishing element of the neutrino mass matrix. The texture has magic and μ − τ symmetry, with a tribimaximal form of the mixing matrix, which leads to θ 13 = 0 that it is not consistent with experimental data and at first, does not seem to be allowed. Since θ 13 a small mixing angle compared to others neutrino mixing angles justifies the use of perturbation theory. We propose that, θ 13, and the Dirac phase δ, and two Majorana phases ρ and σ could be generated by using a complex symmetric perturbation mass matrix in the mass basis and find that affect to the atmospheric mixing angle. We show that only the predictions of the case I, with Δ < 0 and , are consistent with the experimental data. Furthermore, the allowed range of our parameter space and complex elements of perturbation mass matrix are found, which led to finding the allowed region of the neutrino masses, the Majorana phases, the effective neutrino mass for the neutrinoless double beta decay, the allowed deviation of θ 23 from 45°, and to predict the normal neutrino mass hierarchy. The predicted region of and θ 23 are in line with the current experimental data which indicate the accuracy of our model and its results. The results of the case II, with Δ > 0 and , are ruled out.

Texture-zero patterns of lepton mass matrices from modular symmetry

Texture zeros in fermion mass matrices have been widely considered in tackling the Standard Model flavour puzzle. In this work, we perform a systematic analysis of texture zeros in lepton mass matrices in the framework of {Gamma}_3^{prime}cong {T}^{prime } modular symmetry. Assuming that the lepton fields transform as irreducible representations of T′, we obtain all possible texture-zero patterns for both charged-lepton and neutrino mass matrices which can be achieved from T′ modular symmetry. We provide representative models for the phenomenologically-viable textures which can accommodate the experimental data. The predictions for lepton mixing angles, CP-violating phases, light neutrino masses and effective neutrino mass relevant for neutrinoless double beta decay, are discussed. We find that the minimal viable lepton model depends on only 7 real free parameters including the modulus τ (the corresponding charged-lepton mass matrix contains 4 vanishing entries, and the neutrino mass matrix has 1 texture zero). Finally, we study in detail three benchmark models, one for each neutrino mass generation mechanism considered (Dirac, Majorana via Weinberg operator and Majorana via minimal type-I seesaw mechanism).

Constraints on Neutrino Mass Matrix with no Majorana Phases

In the basis where charged lepton mass matrix is real and diagonal, we havefound conditions under which there are no Majorana phases in neutrino massmatrix. An important feature of the condition is that it has been formulatedin terms of modulus of the elements of neutrino mass matrix independent ofphases. If these conditions are satisfied, a CKM type matrix is enough tomake neutrino Majorana mass matrix real and diagonal without any need ofMajorana phases. As an application, we explore the possibility of Majoranaphases in all phenomenologically acceptable neutrino mass matrices with twotexture zeros.

Deviation to the Tri-Bi-Maximal flavor pattern and equivalent classes

In the model-independent context, the neutrino mass matrix is assumed to be diagonalized by means of a unitary matrix that possesses the Tri-Bi-Maximal (TBM) flavor mixing pattern. We present an analysis where the TBM deviation is explored by considering different forms with texture zeros, for the charged lepton mass matrix. These last mass matrices are classified into equivalent classes. We are interested in the charged lepton mass matrices with the minimum free parameter number, i.e. the maximum number of texture zeros, that allows us to correctly reproduce the reactor mixing angle value. We show a deviation from the TBM pattern in terms of the charged lepton masses as well as the theoretical expressions and their parameter space for the mixing angles. Finally, we present the phenomenological implications of numerical values of the “Majorana-like” phase factors on the neutrinoless double-beta decay.

Two-Zero Textures Based on A4 Symmetry and Unimodular Mixing Matrix

We propose a phenomenological model of two-zeros Majorana neutrino mass matrix based on the A4 symmetry, where the structure of mixing matrix is a unimodular second scheme of trimaximal TM2, and the charged lepton mass matrix is diagonal. We show that, among seven possible two-zero textures with A4 symmetry, only two textures, namely the texture with Mee=0 and Meμ=0 and its permutation, are acceptable in the non-perturbation method, since the results associated with these two textures are consistent with the experimental data. We obtain a unique relation between our phases, namely ρ+σ=ϕ±π, and an effective equation sin2θ13=23Rν where Rν=δm2Δm2. Then, only by using the experimental ranges of Rν, we obtain the allowable range of the unknown parameter ϕ as the phase of TM2 mixing matrix, which leads to obtaining not only the ranges of all neutrino oscillation parameters of the model (which agree well with experimental data) but also with the masses of neutrinos, the Dirac and Majorana phases and the Jarlskog parameter, and to predict the normal neutrino mass hierarchy. Finally, we show that all the predictions regarding our two specific textures agree with the corresponding data reported from neutrino oscillation, cosmic microwave background and neutrinoless double beta decay.

Neutrino mass and lepton flavor violation in A4-based left–right symmetric model with linear seesaw

We explore an [Formula: see text] flavor-based left–right symmetric model where neutrino masses and mixing are explained through linear seesaw mechanism. Taking [Formula: see text] flavor symmetry and left–right gauge symmetry together and adding a low-scale seesaw mechanism gives the advantage of (a) getting diagonal structures for both charged lepton mass matrix and Dirac neutrino mass matrix, (b) simpler relations among neutrino observables in the model and (c) large light-heavy neutrino mixing which gives dominant contributions to various lepton flavor violating decays like [Formula: see text], [Formula: see text], [Formula: see text]. By saturating the experimental bounds on these decays we derive constraints on input model parameters and study analytically as well as numerically the correlation among model parameters and their dependence on experimentally determined neutrino parameters like [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We also study CP-violation via Jarlskog invariants and show extra contributions to CP-violating effects that the model generates due to unitarity violation in the neutrino sector.

Time evolution of lepton number carried by Majorana neutrinos

Abstract We revisit the time evolution of the lepton family number for an SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the left-handed current of the neutrino family. For this work we assume that the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number evolves. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and non-relativistic neutrinos. The non-relativistic region is of particular interest for the cosmic neutrino background predicted from Big Bang models. In that region we find that the lepton family numbers are sensitive to the Majorana and Dirac phases, the absolute mass, and the mass hierarchy of neutrinos.

RETRACTED: Lepton number violation in a unified framework

Abstract We study the time evolution of lepton family number for a neutrino that forms an SU(2) doublet with a charged lepton. The lepton family number is defined through a weak basis of the SU(2) doublet in which the charged lepton mass matrix is a real and diagonal one. The lepton family number carried by the neutrino is defined with a left-handed current of the neutrino family. We study the time evolution of the lepton family number operator for the Majorana neutrino. To be definite, we introduce the mass term at $t=0$ and study the time evolution of the lepton family number for the later time. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the flavor eigenstates are related to those of the mass eigenstates. The total lepton number of the Majorana neutrino is conserved. By choosing a specific flavor eigenstate of the neutrino as an initial state, we compute the time evolution of all lepton family numbers. They are sensitive to Majorana and Dirac phases and are also sensitive to the absolute mass and mass hierarchy of neutrinos.

A modular A4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix

We show how to realize two-zero textures of the Majorana neutrino mass matrix Mν based on modular A4 invariant models without flavons. In these models, all matter fields are assigned to three inequivalent singlets, 1, 1′ and 1″, of the finite modular group Γ3≃A4. Considering tensor products of the A4 group, it is easy to make the charged lepton mass matrix Mℓ diagonal. Since not all modular forms of a specific weight and level 3 can be arranged into three inequivalent singlets of A4 simultaneously, we can always make some entries in Mν vanish by properly assigning the representations and modular weights for the matter fields. We consider two cases where neutrino masses originate from the Weinberg operator and the type-I seesaw mechanism, respectively. For the former case, all seven viable two-zero textures of Mν (A1,2, B1,2,3,4 and C) can be realized successfully. For the latter case, only five of them (namely A1,2, B3,4 and C) can be achieved due to the intrinsic structure of the right-handed neutrino mass matrix MR in our assumption for simplicity.

CP symmetries as guiding posts: Revamping tribimaximal mixing. II.

In this follow up of arXiv:1812.04663 we analyze the generalized CP symmetries of the charged lepton mass matrix compatible with the complex version of the Tri-Bi-Maximal (TBM) lepton mixing pattern. These symmetries are used to `revamp' the simplest TBM \textit{Ansatz} in a systematic way. Our generalized patterns share some of the attractive features of the original TBM matrix and are consistent with current oscillation experiments. We also discuss their phenomenological implications both for upcoming neutrino oscillation and neutrinoless double beta decay experiments.

Compatibility of A_{4} flavour symmetric minimal extended seesaw with (3+1) neutrino data

Motivated by the recent resurrection of the evidence for an eV scale sterile neutrino from the MiniBooNE experiment, we revisit one of the most minimal seesaw model known as the minimal extended seesaw that gives rise to a 3+1 light neutrino mass matrix. We consider the presence of A_{4} flavour symmetry which plays a non-trivial role in generating the structure of the neutrino mass matrix. Considering a diagonal charged lepton mass matrix and generic vacuum alignments of A_{4} triplet flavons, we classify the resulting mass matrices based on their textures. Keeping aside the disallowed texture zeros based on earlier studies of 3+1 neutrino textures, we categorise the remaining ones based on texture zeros, mu –tau symmetry in the 3times 3 block and hybrid textures. After pointing out the origin of such 3+1 neutrino textures to A_{4} vacuum alignments, we use the latest 3+1 neutrino oscillation data and numerically analyse the texture zeros and mu –tau symmetric cases. We find that a few of them are allowed from each category predicting interesting correlations between neutrino parameters. We also find that all of these allowed cases prefer normal hierarchical pattern of light neutrino masses over inverted hierarchy.

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.

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.

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.

Group-theoretical search for rows or columns of the lepton mixing matrix

We have used the SmallGroups library of groups, together with the computer algebra systems GAP and Mathematica, to search for groups with a three-dimensional irreducible representation in which one of the group generators has a twice-degenerate eigenvalue while another generator has non-degenerate eigenvalues. By assuming one of these group generators to commute with the charged-lepton mass matrix and the other one to commute with the neutrino (Dirac) mass matrix, one derives group-theoretical predictions for the moduli of the matrix elements of either a row or a column of the lepton mixing matrix. Our search has produced several realistic predictions for either the second row, or the third row, or for any of the columns of that matrix.

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.

Implications of general lepton mass matrices in the standard model on mee

Within the framework of the standard model (SM), using the facility of weak basis (WB) transformations, the general Dirac neutrino mass matrix and the charged lepton mass matrix can essentially be considered as texture two zero mass matrices. Using type I seesaw formula for Majorana neutrino mass matrix, our analysis yields lower bounds ${m}_{ee}\ensuremath{\gtrsim}0.001\text{ }\text{ }\mathrm{eV}$ for normal mass ordering and ${m}_{ee}\ensuremath{\gtrsim}0.08\text{ }\text{ }\mathrm{eV}$ for inverted mass ordering, the latter being tantalizingly close to the expected outcome of the ongoing experiments. Interestingly, for inverted mass ordering, ${m}_{ee}$ is largely independent of variation of mass ${m}_{3}$, whereas, for normal mass ordering with ${m}_{1}$ in the range 0.0001 eV--0.01 eV, the bound on parameter ${m}_{ee}$ gets further sharpened and one obtains ${m}_{ee}$ within the band 0.014--0.042 eV. Further, noting that a particular set of texture four zero quark mass matrices has been shown to be a unique viable option for the description of quark mixing data, an analysis of similar mass matrices in the lepton sector has also been carried out to obtain bounds for the parameter ${m}_{ee}$ with interesting consequences.