Majorana Neutrino Mass Matrix Research Articles

Consequences of the μ−τ reflection symmetry for leptogenesis in a seesaw model with diagonal Dirac neutrino mass matrix

In this paper, we have studied the consequences of the μ−τ reflection symmetry for leptogenesis in the type-I seesaw model with diagonal Dirac neutrino mass matrix. We have first obtained the phenomenologically allowed values of the model parameters, which show that there may exist zero or equal entries in the Majorana mass matrix for the right-handed neutrinos, and then studied their predictions for three right-handed neutrino masses, which show that there may exist two nearly degenerate right-handed neutrinos. Then, we have studied the consequences of the model for leptogenesis. Due to the μ−τ reflection symmetry, leptogenesis can only work in the two-flavor regime. Furthermore, leptogenesis cannot work for the particular case of r=1. Accordingly, for some benchmark values of r≠1, we have given the constraints of leptogenesis for relevant parameters. Furthermore, we have investigated the possibilities of leptogenesis being induced by the renormalization group evolution effects for two particular scenarios. For the particular case of r=1, the renormalization group evolution effects will break the orthogonality relations among different columns of MD and consequently induce leptogenesis to work. For the low-scale resonant leptogenesis scenario which is realized for nearly degenerate right-handed neutrinos, the renormalization group evolution effects can break the μ−τ reflection symmetry and consequently induce leptogenesis to work. Published by the American Physical Society 2024

Neutrino phenomenology in a model with generalized CP symmetry within type-I seesaw framework

We investigate the consequences of generalized CP (GCP) symmetry within the context of the two Higgs doublet model (2HDM), specifically focusing on the lepton sector. Utilizing the type-I seesaw framework, we study an intriguing connection between the Dirac Yukawa couplings originating from both Higgs fields, leading to a reduction in the number of independent Yukawa couplings and simplifying the scalar and Yukawa sectors when compared to the general 2HDM. The constraints coming from CP symmetry of class three (CP3) results in two right-handed neutrinos having equal masses and leads to a diagonal right-handed Majorana neutrino mass matrix. Notably, CP symmetry experiences a soft breaking due to the phase associated with the vacuum expectation value of the second Higgs doublet. The model aligns well with observed charged lepton masses and neutrino oscillation data, explaining both masses and mixing angles, and yields distinct predictions for normal and inverted neutrino mass hierarchies. It features a novel interplay between atmospheric mixing angle θ23 and neutrino mass hierarchy: The angle θ23 is below maximal for the normal hierarchy and above maximal for inverted hierarchy. Another interesting feature of the model is inherent CP violation for the inverted hierarchy. Published by the American Physical Society 2024

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.

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.

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 MASSES IN A LEFT-RIGHT MODEL WITH A LIGHT NEUTRINO MIRROR

In the framework of the extension of the Standard Model with gauge symmetry $SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^{\prime}}$ and additional exotic fermions known as mirror fermions, neutrino masses and mixing are studied. Starting from the most general Majorana neutrino mass matrix, we explore the possibility that one neutrino mirror plays the role of a sterile neutrino with mass on the scale of a few $eV's $, that is, $\hat{m}_1 \approx O(1\: eV)$.

Gauged U(1)Lμ−Lτ symmetry and two-zero textures of inverse neutrino mass matrix in light of muon (g − 2)

In the framework of anomaly free [Formula: see text] model, singlet scalar field with nonzero [Formula: see text] charge gives rise to massive gauge boson [Formula: see text] through spontaneous symmetry breaking. [Formula: see text] leads to one loop contribution to the muon anomalous magnetic moment. These scalar fields may, also, appear in the structure of right-handed neutrino mass matrix, thus, connecting the possible explanation of muon [Formula: see text] and low-energy neutrino phenomenology through vevs associated with the scalar fields. In this work, we consider textures of inverse neutrino mass matrix [Formula: see text] wherein any two elements of the mass matrix are zero. In this ansatz, with Dirac neutrino mass matrix diagonal, the zero(s) of right-handed Majorana neutrino mass matrix correspond to zero(s) in the low-energy effective neutrino mass matrix (within Type-I seesaw). We have realized two such textures of [Formula: see text] accommodating the muon [Formula: see text] and low-energy neutrino phenomenology. The requirement of successful explanation of muon [Formula: see text], further, constrains the allowed parameter space of the model and results in sharp correlations amongst neutrino mixing angles and CP invariants. The model explains muon [Formula: see text] for [Formula: see text] in the range (0.035–0.100 GeV) and [Formula: see text] which is found to be consistent with constraints coming from the current experiments CCFR, COHERENT, BABAR while being within sensitivities of future experiments such as NA62 and NA64.

Investigation of a kind of neutrino mass matrix

We carry out diagonalization of a kind of Majorana neutrino mass matrix of which the real part and imaginary part are commutative. For the matrix M, it is shown in a model-independent way that δ = ±π/2, which implies the maximal strength of CP violation in neutrino oscillations and atmospherical mixing angle would be in the ranges, π/4 < θ 23 < 3π/4, or −3π/4 < θ 23 < −π/4. It is shown that the Hermitian Majorana neutrino mass matrix M has only five real parameters and furthermore, only one free real parameter (A or D) if using the measured values of three mixing angles and mass squared differences as inputs.

Small 𝜃13 and solar neutrino oscillation parameters from μ − τ symmetry

Exchange [Formula: see text] symmetry in the effective Majorana neutrino mass matrix does predict a maximal mixing for atmospheric neutrino oscillations asides to a null mixing that cannot be straightforwardly identified with reactor neutrino oscillation mixing, [Formula: see text], unless a specific ordering is assumed for the mass eigenstates. Otherwise, a nonzero value for [Formula: see text] is predicted already at the level of an exact symmetry. In this case, solar neutrino mixing and scale, as well as the correct atmospheric mixing arise from the breaking of the symmetry. I present a mass matrix proposal for normal hierarchy that realizes this scenario, where the smallness of [Formula: see text] is naturally given by the parameter [Formula: see text] and the solar mixing is linked to the smallness of [Formula: see text]. The proposed matrix remains stable under renormalization effects and it also allows to account for CP violation within the expected region without further constrains.

Scalar dark matter in the A4-based texture one-zero neutrino mass model within the inverse seesaw mechanism

Abstract In this paper, we present a model based on A4 discrete flavor symmetry implementing inverse and type-II seesaw mechanisms to have LHC-accessible TeV-scale right-handed neutrino mass and texture one-zero in the resulting Majorana neutrino mass matrix, respectively. We investigate the neutrino and dark matter sectors of the model. Non-Abelian discrete A4 symmetry spontaneously breaks into the Z2 subgroup and hence provides a stable dark matter candidate. To constrain the Yukawa Lagrangian of our model, we impose $Z^{\prime }_2$, Z3, and Z4 cyclic symmetries in addition to the A4 flavor symmetry. In this work we use the recently updated data on cosmological parameters from the Planck Collaboration [N. Aghanim et al. [Planck Collaboration], Astron. Astrophys. A6, 641 (2020)]. For the dark matter candidate mass around 45–55 GeV, we obtain a mediator particle mass (right-handed neutrinos) ranging from 138–155 GeV. The Yukawa couplings are found to be in the range 0.995–1 to have observed the relic abundance of dark matter. We further obtain inverse ($X\equiv \frac{F^2n}{z^2}$) and type-II ($X^{\prime}\equiv f_1 v_{\Delta _{1}}$) seesaw contributions to the 0νββ decay amplitude |Mee|, with the model being consistent with low-energy experimental constraints. In particular, we emphasize that the type-II seesaw contribution to |Mee| is large compared to the inverse seesaw contribution for normally ordered (NO) neutrino masses.

Texture of one equality in neutrino mass matrix

We carry out a phenomenological and analytical study of the texture structures for the Majorana neutrino mass matrix characterized by one single equality between two independent matrix elements, with vanishing non-physical phases whose role in the definition we clarify. We find that fourteen textures are viable in both types of hierarchy, whereas the remaining fifteenth one is viable only in normal hierarchy. We also present symmetry realizations for some patterns by using Abelian flavor symmetries within type-I, type-II and mixed type-(I+II) seesaw scenarios.

Noncommutative geometry, the Lorentzian standard model, and its B−L extension

We explore the 1-loop renormalization group flow of two models coming from a generalization of the Connes-Lott version of Noncommutative Geometry in Lorentzian signature: the Noncommutative Standard Model and its B-L extension. Both make predictions on coupling constants at high energy, but only the latter is found to be compatible with the top quark and Higgs boson masses at the electroweak scale. We took into account corrections introduced by threshold effects and the relative positions of the Dirac and Majorana neutrino mass matrices and found them to be important. Some effects of 2-loop corrections are briefly discussed. The model is consistent with experiments only for a very small part of its parameter space and is thus predictive. The masses of the $Z'$ and B-L breaking scalar are found to be of the order $10^{14}$ GeV.

CP odd weak basis invariants in minimal see-saw model and leptogenesis

Abstract In this paper, we derive the relationship between the weak basis invariants (WB) related to CP violation responsible for leptogenesis and CP violation relevant at low energy. We examine all the experimentally viable cases of Frampton-Glashow and Yanagida (FGY) model, in order to construct the WB invariants in terms of left handed Majorana neutrino mass matrix elements, and thus finding the necessary and sufficient condition for CP conservation. Further for all the viable FGY texture zeros, we have shown the explicit dependence of WB invariants on Dirac type and Majorana type CP violating phases. In the end, we discuss the implication of such interrelationships on leptogenesis.

Implications of CP invariants for the flavored hybrid neutrino mass matrix

Abstract We re-examine the weak basis invariants at low energies proposed by C. Jarlskog and Branco et al. in their earlier analyses, after confronting them with the assumptions of two zeros and an equality between arbitrary non-zero elements in the Majorana neutrino mass matrix in the flavored basis. This particular conjecture is found to be experimentally feasible, as shown by S. Dev and D. Raj in their recent work. The present analysis attempts to find the necessary and sufficient condition for CP invariance for each experimentally viable ansatz pertaining to the model, along with some important implications.

Minimal extended seesaw and group symmetry realization of two-zero textures of neutrino mass matrices

We study the phenomenology of two-zero textures of Mν4×4 neutrino mass matrices in the minimal extended seesaw (MES) mechanism. Mν4×4 involves 3×3 Dirac neutrino mass matrix (MD), 3×3 right-handed Majorana neutrino mass matrix MR and 1×3 matrix MS that couples the singlet field ‘S’ with the right-handed neutrinos. We consider the phenomenologically predictive cases (5+3) and (6+2) schemes for zero textures of MD and MR of 3×3 active sector of Mν4×4 along with admissible one or two-zero textures of MS. Although there is a large number of combinations of MD,MR and MS leading to the desired two-zero textures, S3 group transformations between the different zero textures of MD,MR and MS reduce them to a small number of basic combinations. In MES, Mν4×4 should be a matrix of rank 3, so we have 12 two-zero textures of neutrino mass matrices of rank 3 out of total 15 two-zero textures of neutrino mass matrices. In realization of the two-zero textures in (5+3) scheme we have obtained a number of correlations among the neutrino mass matrix elements mij, while none of the two-zero textures could be realized in the (6+2) scheme. The viability of each of the realizable textures is checked by plotting the scatter plots of their respective correlations under the current neutrino oscillation data. We have analysed the role played by the Dirac and Majorana CP phases for each of the textures. For constrained ranges of CP phases we also draw scatter plots for Jarlskog invariant (JCP) and effective electron neutrino mass |mββ|. In our study the viable textures are finally realized by Z8 Abelian group symmetry by extending the Standard Model to include few scalar fields.

New hybrid textures for neutrino mass matrices

We perform a systematic investigation of the texture structures of Majorana neutrino mass matrix Mν having two texture zeros and an equality between two nonzero matrix elements, in the light of recent neutrino oscillation data. Among forty-two possible textures, it is found that only eight textures are compatible with the current experimental data at 3σ C.L. Out of these phenomenologically viable textures, six follow normal mass ordering while remaining two satisfy the inverted mass ordering of neutrino mass spectrum. In the numerical analysis, we carry out a scan over the possible space of all viable patterns. We present the implications of each allowed patterns for three mixing angles (solar, reactor and atmospheric), leptonic CP-violation, neutrino mass scale and the neutrinoless double beta decay indicating strong correlations between oscillation parameters. The symmetry realization of one of the viable textures is also presented.

Parametrized leptogenesis from linear seesaw

We present a purely linear seesaw mechanism in a mirror left-right symmetric framework and then realize a novel leptogenesis scenario for parametrizing the cosmic baryon asymmetry by the charged lepton masses, the light Majorana neutrino mass matrix and the heavy mirror charged lepton masses. Through the same Yukawa couplings, the lepton-number-conserving decays of the mirror charged leptons can generate three individual lepton asymmetries stored in the ordinary lepton flavors, while the lepton-number-violating processes for the Majorana neutrino mass generation can wash out part of these lepton asymmetries. The remnant lepton asymmetries then can be partially converted to a baryon asymmetry by the sphaleron processes.

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.

Baryon asymmetry from left-right phase transition

We extend the standard model fermions by a mirror copy to realize a left-right symmetry. During a strongly first order phase transition of the spontaneous left-right symmetry breaking, the CP-violating reflections of the mirror fermions off the mirror Higgs bubbles can generate a mirror lepton asymmetry and an equal mirror baryon asymmetry. We then can obtain an ordinary baryon asymmetry through the mirror fermion decays where a dark matter scalar plays an essential role. Benefitted from a parity symmetry for solving the strong CP problem, the cosmic baryon asymmetry can be well described by the ordinary lepton mass matrices up to an overall factor. In this scenario, the Dirac CP phase in the Majorana neutrino mass matrix can provide a unique source for the required CP violation. Furthermore, the Higgs triplet for type-II seesaw as well as the first generation of mirror charged fermions can be allowed at the TeV scale.