Lepton Mass Matrices Research Articles

Tension between neutrino masses and gauge coupling unification in natural grand unified theories

The natural grand unified theories (GUT) solve various problems of the supersymmetric GUT and give realistic quark and lepton mass matrices under the natural assumption that all terms allowed by the symmetry are introduced with O(1) coefficients. However, because of the natural assumption, it is difficult to achieve the gauge coupling unification without tuning, while keeping neutrino masses at realistic values. In this paper, we try to avoid this tension between the neutrino masses and the gauge coupling unification, by introducing suppression factors for several terms. These suppression factors can be understood by approximate symmetries in some of the solutions. We show that one of the most important results in the natural GUT scenario, that the nucleon decay mediated by superheavy gauge fields is enhanced due to a smaller unification scale while the nucleon decay mediated by superheavy colored Higgs is suppressed, may change in those models proposed in this paper. Published by the American Physical Society 2024

Tri-Bi-Maximal flavor pattern deviation using equivalent class

We assume that the neutrino mass matrix Mν, in the model-independent context, is diagonalized by the Tri-Bi-Maximal (TBM) pattern. In the following, we explore the TBM mixing pattern deviation by considering different textures for the charged lepton matrix, which are classified into equivalence classes that allow us to reproduce the experimental data on neutrino oscillation. Our target is on the charged lepton matrix with the minimum number of free parameters, i.e., the maximum number of zeros of the texture that allows us to correctly reproduce the value of the reactor mixing angle θ13. We show a deviation from the TBM pattern in terms of the charged leptonic masses, which provides a prediction value for the phase factors in the charged lepton mass matrices. These are related to the “Dirac-like” CP and “Majorana-like” phase factors. For the last type of phase, we show its phenomenological implications through effective Majorana mass in the neutrinoless double-beta decay.

Non-SUSY lepton flavor model with the three Higgs doublet model

Abstract We propose a simple non-supersymmetric lepton flavor model with A4 symmetry. The A4 group is a minimal one that includes triplet irreducible representation. We introduce three Higgs doublets, which are assigned as a triplet of the A4 symmetry. It is natural that there are three generations of the Higgs fields, as with the standard model fermions. We analyze the potential and find the vacuum expectation values for the local minimum. In the vacuum expectation values, we obtain the charged lepton, Dirac neutrino, and right-handed Majorana neutrino mass matrices. By using the type-I seesaw mechanism, we get the left-handed Majorana neutrino mass matrix. In the NuFIT 5.1 data, we predict the Dirac CP phase and the Majorana phases for the only inverted neutrino mass hierarchy. In particular, the Dirac CP phase and lepton mixing angle θ23 are strongly correlated. If θ23 is more precisely measured, the Dirac CP phase is more precisely predicted, and vice versa. We also predict the effective mass for neutrinoless double beta decay mee ≃ 47.1 [meV] and the lightest neutrino mass m3 ≃ 0.789–1.43 [meV]. This will be testable with our model in near-future neutrino experiments.

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.

Flavor structures of quarks and leptons from flipped SU(5) GUT with A4 modular flavor symmetry

We propose to generate the flavor structures of the Standard Model plus neutrinos from flipped SU(5) GUT with A4 modular flavor symmetry. Possible way to assign different moduli values for quarks and leptons in modular GUT scheme is discussed. We propose to reduce the multiple modular symmetries to a single modular symmetry in the low energy effective theory with proper boundary conditions. We classify all possible scenarios in this scheme according to the assignments of the modular A4 representations for matter superfields and give the expressions of the quark and lepton mass matrices predicted by our scheme at the GUT scale. After properly selecting the modular weights for various superfields that can lead to better fitting, we can obtain the best-fit points with the corresponding χ2 values for the sample subscenarios. We find that the flavor structures of the Standard Model plus neutrinos can be fitted perfectly in such a A4 modular flavor GUT scheme with single or two modulus fields. Especially, the {chi}_{textrm{total}}^2 of our fitting can be as low as 1.558 for sample IX′ of scenario III even if only a single common modulus field for both quark and lepton sectors is adopted. The most predictive scenario III, in which all superfields transform as triplets of A4, can be fitted much better with two independent moduli fields τq, τl for quark sector and lepton sector ( {chi}_{textrm{total}}^2 ≈ 95) than that with the single modulus case ( {chi}_{textrm{total}}^2 ≈ 282.4).

Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points

We study quark and lepton mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Quark and lepton masses have a large hierarchy. In addition, mixing angles are large in the lepton sector, while those are small in the quark sector. We find that this structure can be realized in certain flavor models, which are identified by the zero points of the zero-mode wave functions of fermions and Higgs modes. We classify such realistic flavor models. Fixed points $\tau=i$, $e^{2\pi i/3}$ and $i\infty$ of the modulus $\tau$ play a role in realizing a large mass hierarchy through our scenario, where residual $S$, $ST$, and $T$ symmetries remain and the lightest Higgs modes can correspond to eigenstates of residual symmetries at the leading order. As a result, we find that there are 24 flavor models in total which can be realistic in a vicinity of $S$-symmetric vacuum but no flavor models for $ST$ and $T$-symmetric vacua.

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.

Hiding neutrinoless double beta decay in the minimal seesaw model with the TM1 or μ–τ reflection symmetry

In Asaka et al (2021 Phys. Rev. D 103, 015014), Asaka, Ishida and Tanaka put forward an interesting possibility that the neutrinoless double beta decay can be hidden in the minimal seesaw model with the two right-handed neutrinos having a hierarchical mass structure: the lighter one is lighter enough than the typical Fermi-momentum scale of nuclei while the heavier one is sufficiently heavy to decouple from the neutrinoless double beta decay. Then, in the basis where the mass matrices of the charged leptons and right-handed neutrinos are diagonal, for some particular texture of the Dirac neutrino mass matrix , the neutrinoless double beta decay can be hidden. In this paper, on top of this specified model, we study the interesting scenario that further obeys the TM1 symmetry or μ–τ reflection symmetry which are well motivated by the experimental results for the neutrino mixing parameters.

Lepton mass matrix from double covering of A 4 modular flavor symmetry* *The work of H. O. is supported by the Junior Research Group (JRG) Program at the Asia-Pacific Center for Theoretical Physics (APCTP) through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government and was supported by the Korean Local Governments-Gyeongsangbuk-do Province and Pohang City.

We study a double covering of modular flavor symmetry. To this end, we construct lepton models for canonical and radiative seesaw scenarios. Using irreducible doublet representations, heavier Majorana fermion masses are characterized by one free parameter that would differentiate from symmetry. symmetry. Through χ square numerical analysis, we demonstrate that both scenarios produce some predictions in case of normal hierarchy reproducing neutrino oscillation data. However, no solution satisfies the neutrino oscillation data in case of radiative seesaw of inverted hierarchy.

A non-renormalizable neutrino mass model with S3 ⊗ Z2 symmetry

The lepton sector is studied within a flavored non-renormalizable model where the S3 ⊗ Z2 flavor symmetry controls the masses and mixings. In this work, the effective neutrino as well as the charged lepton mass matrices are hierarchical and these have (under a benchmark in the charged sector) a kind of Fritzsch textures that accommodate the mixing angles in good agreement with the last experimental data. The model favors the normal hierarchy, this also predicts consistent values for the CP-violating phase and the |mee| effective Majorana neutrino mass rate. Along with this, the branching ratio for the lepton flavor violation process, µ → eγ, is below the current bound.

Modular symmetry in the SMEFT

We study the modular symmetric standard model effective field theory. We employ the stringy Ansatz on coupling structure that 4-point couplings ${y}^{(4)}$ of matter fields are written by a product of 3-point couplings ${y}^{(3)}$ of matter fields, i.e., ${y}^{(4)}={y}^{(3)}{y}^{(3)}$. In this framework, we discuss the flavor structure of bilinear fermion operators and 4-fermion operators, where the holomorphic and antiholomorphic modular forms appear. From the Ansatz, the ${A}_{4}$ modular-invariant semileptonic four-fermion operator $[{\overline{E}}_{R}\mathrm{\ensuremath{\Gamma}}{E}_{R}][{\overline{D}}_{R}\mathrm{\ensuremath{\Gamma}}{D}_{R}]$ does not lead to the flavor changing (FC) processes since this operator would be constructed in terms of gauge couplings $g$ as ${y}^{(3)}\ensuremath{\sim}g$. The chirality flipped bilinear operator $[{\overline{D}}_{R}\mathrm{\ensuremath{\Gamma}}{D}_{L}]$ also does not lead FC if the mediated mode corresponds to the Higgs boson ${H}_{d}$. In this case, the flavor structure of this operator is the exactly same as the mass matrix. On the other hand, if the flavor structure of the operator is not the exactly same as the mass matrix, the situation would change drastically. Then, we obtain the nontrivial relations of FC transitions at nearby fixed points $\ensuremath{\tau}=i,\ensuremath{\omega},i\ensuremath{\infty}$, which are testable in the future. As an application, we discuss the relations of the lepton flavor violation processes $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma},\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ at nearby ${\ensuremath{\tau}}_{e}=i$, where the successful lepton mass matrix was obtained. We also study the flavor changing 4-quark operators in the ${A}_{4}$ modular symmetry of quarks. As a result, the minimal flavor violation could be realized by taking relevant specific parameter sets of order one.

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.

SO(10) models with A4 modular symmetry

We combine SO(10) Grand Unified Theories (GUTs) with A4 modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of Γ3 ≃ A4, with a Higgs sector comprising a single Higgs multiplet H in the 10 fundamental representation and one Higgs field overline{Delta } in the overline{mathbf{126}} for the minimal models, plus one Higgs field Σ in the 120 for the non-minimal models, all with specified modular weights. The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data. For the phenomenologically successful models, we present the best fit results in numerical tabular form as well as showing the most interesting graphical correlations between parameters, including leptonic CP phases and neutrinoless double beta decay, which have yet to be measured, leading to definite predictions for each of the models.

TeV scale resonant leptogenesis with Lμ−Lτ gauge symmetry in light of the muon g−2

Motivated by the growing evidence for the possible lepton flavour universality violation after the first results from Fermilab's muon $(g-2)$ measurement, we revisit one of the most widely studied anomaly free extensions of the standard model namely, gauged $L_{\mu}-L_{\tau}$ model, to find a common explanation for muon $(g-2)$ as well as baryon asymmetry of the universe via leptogenesis. The minimal setup allows TeV scale resonant leptogenesis satisfying light neutrino data while the existence of light $L_{\mu}-L_{\tau}$ gauge boson affects the scale of leptogenesis as the right handed neutrinos are charged under it. For $L_{\mu}-L_{\tau}$ gauge boson mass at GeV scale or above, the muon $(g-2)$ favoured parameter space is already ruled out by other experimental data while bringing down its mass to sub-GeV regime leads to vanishing lepton asymmetry due to highly restrictive structures of lepton mass matrices at the scale of leptogenesis. Extending the minimal model with two additional Higgs doublets can lead to a scenario consistent with successful resonant leptogenesis and muon $(g-2)$ while satisfying all relevant experimental data.

Electron EDM arising from modulus \u03c4 in the supersymmetric modular invariant flavor models

The electric dipole moment (EDM) of electron is studied in the supersymmetric A4 modular invariant theory of flavors with CP invariance. The CP symmetry of the lepton sector is broken by fixing the modulus τ. Lepton mass matrices are completely consistent with observed lepton masses and mixing angles in our model. In this framework, a fixed τ also causes the CP violation in the soft SUSY breaking terms. The electron EDM arises from the CP non-conserved soft SUSY breaking terms. The experimental upper bound of the electron EDM excludes the SUSY mass scale below 4–6 TeV depending on five cases of the lepton mass matrices. In order to see the effect of CP phase of the modulus τ, we examine the correlation between the electron EDM and the decay rate of the μ → eγ decay, which is also predicted by the soft SUSY breaking terms. The correlations are clearly predicted in contrast to models of the conventional flavor symmetry. The branching ratio is approximately proportional to the square of |de/e|. The SUSY mass scale will be constrained by the future sensitivity of the electron EDM, |de/e| ≃ 10−30 cm. Indeed, it could probe the SUSY mass range of 10–20 TeV in our model. Thus, the electron EDM provides a severe test of the CP violation via the modulus τ in the supersymmetric modular invariant theory of flavors.

Implications of the Muon g-2 result on the flavour structure of the lepton mass matrix

The confirmation of the discrepancy with the Standard Model predictions in the anomalous magnetic moment by the Muon g-2 experiment at Fermilab points to a low scale of new physics. Flavour symmetries broken at low energies can account for this discrepancy but these models are much more restricted, as they would also generate off-diagonal entries in the dipole moment matrix. Therefore, if we assume that the observed discrepancy in the muon g-2 is explained by the contributions of a low-energy flavor symmetry, lepton flavour violating processes can constrain the structure of the lepton mass matrices and therefore the flavour symmetries themselves predicting these structures. We apply these ideas to several discrete flavour symmetries popular in the leptonic sector, such as Delta (27), A_4, and A_5 < imes mathrm{CP}.

Neutrino mass observables and non-Hermitian version of Type-I seesaw model

We study the non-Hermitian extension of the Lagrangian of the Standard Model extended by singlet right-handed heavy neutrinos. The Yukawa coupling matrices comprise of Hermitian and non-Hermitian components and the neutrino mass eigenvalues are calculated for three generation case. The increased number of unknown parameters in the theory due to non-Hermitian nature of coupling matrices impose problem for its productiveness. Hence we apply four zero texture for the Yukawa matrices. We consider the normal hierarchy of neutrino mass ordering and find the mixing angles and Dirac CP violating phase by diagonalizing the lepton mass matrices. The parameters of the mixing matrix are obtained in terms of the parameters of the non-Hermitian Yukawa coupling matrix. The values of the angles and phase are compatible with experimental data available for neutrino mass observables and using this the non-Hermitian parameters are constrained.