A4 Flavor Symmetry Research Articles

Dirac CP violation phase in the neutrino sector with A4 flavour symmetry

Dear Editors, On behalf of all co-authors i would like to submit our paper entitled " Dirac CP violation phase in the neutrino sector with A4 flavour symmetry " for publication in the VNU Journal ò Science: Mathematics and Physics. Looking forward to hearing from you. With best regards, Trần Tiến Mạnh

Neutrino mass sum rules from modular A4 symmetry

Modular symmetries offer a dynamic approach to understanding the flavor structure of leptonic mixing. Using the modular A4 flavor symmetry integrated in a type-II seesaw, we propose a simple and minimalistic model that restricts the neutrino oscillation parameter space and, most importantly, introduces a sum rule in the physical neutrino masses. When combined with the mass squared differences observed in neutrino oscillations, this sum rule determines the absolute neutrino mass scale. This has significant implications for cosmology, neutrinoless double beta decay experiments, and direct neutrino mass measurements. In particular, the model predicts ∑imi≈0.1 eV for both normal and inverted ordering, and thus can be fully probed by the current generation of cosmological probes in the upcoming years. Published by the American Physical Society 2024

Muon [formula omitted], dark matter, and neutrino mass explanations in a modular [formula omitted] symmetry

We study a successful model to explain the muon anomalous magnetic moment originating from Yukawa-type interactions in a supersymmetric theory. Thanks to a modular A4 flavor symmetry, any lepton flavor violations that spoil the model are forbidden. We also investigate a predictive radiative seesaw model including a dark matter (DM) candidate. At first, we construct the minimum model to satisfy the neutrino oscillation data and obtain several predictions such as Dirac CP and Majorana phases, the neutrino masses through χ2 analysis. However, the minimum model would not provide our promising DM candidate. Thus, we minimally extend the model and find a good DM candidate. In the extended framework, we show the allowed regions to satisfy the muon anomalous magnetic moment and the observed relic density of dark matter in addition to predictions of the lepton sector.

Discrete dark matter mechanism as the source of neutrino mass scales

The hierarchy in scale between atmospheric and solar neutrino mass splittings is investigated through two distinct neutrino mass mechanisms from tree-level and one-loop-level contributions. We demonstrate that the minimal discrete dark matter mechanism contains the ingredients for explaining this hierarchy. This scenario is characterized by adding new RH neutrinos and SU(2)-doublet scalars to the Standard Model as triplet representations of an A4 flavor symmetry. The A4 symmetry breaking, which occurs at the electroweak scale, leads to a residual ℤ2 symmetry responsible for the dark matter stability and dictates the neutrino phenomenology. Finally, we show that to reproduce the neutrino mixing angles correctly, it is necessary to violate CP in the scalar potential.

Exploring the feasibility of the charged lepton flavor violating decay μ → e + γ in inverse and linear seesaw mechanisms with A4 flavor symmetry

One of the possible ways to explain the observed flavor structure of fundamental particles is to include flavor symmetries in the theories. In this work, we investigate the rare charged lepton flavor violating (cLFV) decay process [Formula: see text] in two of the low-scale ([Formula: see text][Formula: see text]TeV) seesaw models: (i) the Inverse seesaw (ISS) and (ii) Linear seesaw (LSS) models within the framework of [Formula: see text] flavor symmetry. Apart from the [Formula: see text] flavor symmetry, some other symmetries like [Formula: see text], [Formula: see text] and [Formula: see text] are included to construct the Lagrangian. We use results from our previous work [M. R. Devi and K. Bora, A comparative study of type-II, inverse and linear seesaw mechanisms with [Formula: see text] flavor symmetry, presented at DAE HEP Symp., 2020, Jatni, Odisha; M. R. Devi and K. Bora, Mod. Phys. Lett. A 37, 2250073] where we computed unknown neutrino oscillation parameters within [Formula: see text] limits of their global best fit values, and apply those results to compute the branching ratio (BR) of the muon decay for both the seesaw models. Next we compare our results with the current experimental bounds and sensitivity limits of BR[Formula: see text] as projected by various experiments, and present a comparative analysis that which of the two models is more likely to be tested by which current/future experiment. This is done for various values of currently allowed non-unitarity parameter. This comparative study will help us to pinpoint that which of the low-scale seesaw models and triplet flavon VEV alignments will be more viable and favorable for testing under a common flavor symmetry ([Formula: see text] here), and hence can help discriminate between the two models.

Five-zero texture in neutrino-dark matter model within the framework of minimal extended seesaw

We study a model of neutrino and dark matter within the framework of a minimal extended seesaw (MES). This model is based on A4 flavour symmetry along with the discrete Z3×Z4 symmetry to stabilize the dark matter and construct desired mass matrices for neutrino mass. Five-zero textures are imposed in the final 4×4 active-sterile mass matrix, which significantly reduces the free parameter in the model. Three right-handed neutrinos were considered, two of them have degenerate masses which help us to achieve baryogenesis via resonant leptogenesis. A singlet fermion (sterile neutrino) with mass ∼O(eV) is also considered, and we are able to put bounds on active-sterile mixing parameters via neutrino oscillation data. Resonant enhancement of lepton asymmetry is studied at the TeV scale, where we discuss a few aspects of baryogenesis considering the flavour effects. The possibility of improvement in effective mass from 0νββ in the presence of a single generation of sterile neutrino flavour is also studied within the fermion sector. In the scalar sector, the imaginary component of the complex singlet scalar (χ) is behaving as a potential dark matter candidate and simultaneously the real part of the complex scalar is associated with the fermion sector for sterile mass generation.

Two A4 modular symmetries for Tri-Maximal 2 mixing

We construct a lepton flavour model based on two A4 modular symmetries. The two A4 are broken by a bi-triplet field to the diagonal A4 subgroup, resulting in an effective modular A4 flavour symmetry with two moduli. We employ these moduli as stabilisers, that preserve distinct residual symmetries, enabling us to obtain Tri-Maximal 2 (TM2) mixing with a minimal field content, flavonless at the effective scale, below the breaking to the single A4.

Octant of 𝜃23, MH, 0νββ decay and vacuum alignment of A4 flavor symmetry in an inverse seesaw model

Measurements of disappearance channel of long baseline accelerator-based experiments (like NO[Formula: see text]A) are inflicted with the problem of octant degeneracy. In these experiments, the mass hierarchy (MH) sensitivity depends upon the value of CP-violating phase [Formula: see text]. Moreover, MH of light neutrino masses is still not fixed. Also, the flavor structure of fermions is yet not fully understood. We discuss all these issues in a highly predictive, low-scale inverse seesaw (ISS) model within the framework of [Formula: see text] flavor symmetry. Recent global analysis has shown a preference for normal hierarchy and higher octant of [Formula: see text], and hence we discuss our results with reference to these, and find that the vacuum alignment of [Formula: see text] triplet flavon [Formula: see text] favors these results. Finally, we check if our very precise prediction on [Formula: see text] and the lightest neutrino mass falls within the range of sensitivities of the neutrinoless double beta decay [Formula: see text] experiments. We note that when octant of [Formula: see text] and MH is fixed by more precise measurements of future experiments, then through our results, it would be possible to precisely identify the favorable vacuum alignment corresponding to the [Formula: see text] triplet field as predicted in our model.

Non-zero θ13 and δCP phase with A4 flavor symmetry and deviations to tri-bi-maximal mixing via Z2 × Z2 invariant perturbations in the neutrino sector

In this work, a flavour theory of a neutrino mass model based on A4 symmetry is considered to explain the phenomenology of neutrino mixing. The spontaneous symmetry breaking of A4 symmetry in this model leads to tribimaximal mixing in the neutrino sector at a leading order. We consider the effect of Z2×Z2 invariant perturbations in neutrino sector and find the allowed region of correction terms in the perturbation matrix that is consistent with 3σ ranges of the experimental values of the mixing angles. We study the entanglement of this formalism on the other phenomenological observables, such as δCP phase, the neutrino oscillation probability P(νμ→νe), the effective Majorana mass |mee| and |mνeeff|. A Z2×Z2 invariant perturbations in this model is introduced in the neutrino sector which leads to testable predictions of θ13 and CP violation. By changing the magnitudes of perturbations in neutrino sector, one can generate viable values of δCP and neutrino oscillation parameters. Next we investigate the feasibility of charged lepton flavour violation in type-I seesaw models with leptonic flavour symmetries at high energy that leads to tribimaximal neutrino mixing. We consider an effective theory with an A4×Z2×Z2 symmetry, which after spontaneous symmetry breaking at high scale which is much higher than the electroweak scale leads to charged lepton flavour violation processes once the heavy Majorana neutrino mass degeneracy is lifted either by renormalisation group effects or by a soft breaking of the A4 symmetry. In this context the implications for charged lepton flavour violation processes like μ→eγ, τ→eγ, τ→μγ are discussed.

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.

Lepton flavor mixing and CP violation in the minimal type-(I+II) seesaw model with a modular A4 symmetry

In this paper, we study the implications of the modular A4 flavor symmetry in constructing a supersymmetric minimal type-(I+II) seesaw model, in which only one right-handed neutrino and two Higgs triplets are introduced to account for the tiny neutrino masses, flavor mixing and CP violation. We consider the most economical case where the right-handed neutrino and the Higgs triplets in this model are assigned into the trivial one-dimensional irreducible representation of the modular group A4, and all the modular forms are with the lowest weights they can take. We find that the octant of the mixing angle θ23 strongly depends on the hierarchy of free model parameters in the charged-lepton sector. We also show that the neutrino mass matrix can possess an approximate μ−τ reflection symmetry for some specific values of free parameters. Moreover, our model predicts relatively large masses of three light neutrinos, thus can be easily tested in future neutrino experiments.

Phenomenological study of neutrino mass, dark matter and baryogenesis within the framework of minimal extended seesaw

We study a model of neutrino and dark matter within the framework of a minimal extended seesaw. This framework is based on A4 flavor symmetry along with the discrete Z4 symmetry to stabilize the dark matter and construct desired mass matrices for neutrino mass. We use a non-trivial Dirac mass matrix with broken μ − τ symmetry to generate the leptonic mixing. A non-degenerate mass structure for right-handed neutrinos is considered to verify the observed baryon asymmetry of the Universe via the mechanism of thermal Leptogenesis. The scalar sector is also studied in great detail for a multi-Higgs doublet scenario, considering the lightest Z4-odd as a viable dark matter candidate. A significant impact on the region of DM parameter space, as well as in the fermionic sector, are found in the presence of extra scalar particles.

Modular S4 and A4 symmetries and their fixed points: new predictive examples of lepton mixing

In the modular symmetry approach to neutrino models, the flavour symmetry emerges as a finite subgroup ΓN of the modular symmetry, broken by the vacuum expec- tation value (VEV) of a modulus field τ. If the VEV of the modulus τ takes some special value, a residual subgroup of ΓN would be preserved. We derive the fixed points τS = i, τST = (−1 + i sqrt{3} )/2, τTS = (1 + i sqrt{3} )/2, τT = i∞ in the fundamental domain which are in-variant under the modular transformations indicated. We then generalise these fixed points to τf = γτS, γτST, γτTS and γτT in the upper half complex plane, and show that it is suffi-cient to consider γ ∈ ΓN. Focussing on level N = 4, corresponding to the flavour group S4, we consider all the resulting triplet modular forms at these fixed points up to weight 6. We then apply the results to lepton mixing, with different residual subgroups in the charged lepton sector and each of the right-handed neutrinos sectors. In the minimal case of two right-handed neutrinos, we find three phenomenologically viable cases in which the light neutrino mass matrix only depends on three free parameters, and the lepton mixing takes the trimaximal TM1 pattern for two examples. One of these cases corresponds to a new Littlest Modular Seesaw based on CSD(n) with n = 1 + sqrt{6} ≈ 3.45, intermediate between CSD(3) and CSD(4). Finally, we generalize the results to examples with three right-handed neutrinos, also considering the level N = 3 case, corresponding to A4 flavour symmetry.

Comment on the article by D. Borah and B. Karmakar “Linear seesaw for Dirac neutrinos with A4 flavour symmetry”, Phys. Lett. B 789 (2019) 59–70, arXiv:1806.10685

D. Borah and B. Karmakar [1] have proposed an A4 flavoured linear seesaw model to realise light Dirac neutrinos. In this comment article, we show that some neutrino Yukawa interactions were missed in the model Ref. [1], thus implying that a different formula would be needed to determine the effective neutrino mass matrix, with significantly different results. Our result shows that, unlike stated in Ref. [1], that the inverted neutrino mass spectrum is not ruled out.

Active and sterile neutrino phenomenology with A4 based minimal extended seesaw

We study a model of neutrino within the framework of minimal extended seesaw (MES), which plays an important role in active and sterile neutrino phenomenology in (3+1) scheme. The A4 flavor symmetry is augmented by additional Z4×Z3 symmetry to constraint the Yukawa Lagrangian of the model. We use non-trivial Dirac mass matrix, with broken μ−τ symmetry, as the origin of leptonic mixing. Interestingly, such structure of mixing naturally leads to the non-zero reactor mixing angle θ13. Non-degenerate mass structure for right-handed neutrino MR is considered so that we can further extend our study to Leptogenesis. We have also considered three different cases for sterile neutrino mass, MS to check the viability of this model, within the allowed 3σ bound in this MES framework.

Linear seesaw for Dirac neutrinos with A4 flavour symmetry

We propose a linear seesaw model to realise light Dirac neutrinos within the framework of A4 discrete flavour symmetry. The additional fields and their transformations under the flavour symmetries are chosen in such a way that naturally predicts the hierarchies of different elements of the seesaw mass matrix and also keeps the unwanted terms away. For generic choices of flavon alignments, the model predicts normal hierarchical light neutrino masses with the atmospheric mixing angle in the lower octant. Apart from predicting interesting correlations between different neutrino parameters as well as between neutrino and model parameters, the model also predicts the leptonic Dirac CP phase to lie in a specific range −π/2≲δ≲−π/5 and π/5≲δ≲π/2 that includes the currently preferred maximal value. The predictions for the absolute neutrino masses in one specific version of the model can also saturate the cosmological upper bound on sum of absolute neutrino masses.

Flavour-symmetric type-II Dirac neutrino seesaw mechanism

We propose a Standard Model extension with underlying A4 flavour symmetry where small Dirac neutrino masses arise from a Type-II seesaw mechanism. The model predicts the “golden” flavour-dependent bottom-tau mass relation, requires an inverted neutrino mass ordering and non-maximal atmospheric mixing angle. Using the latest neutrino oscillation global fit [1] we derive restrictions on the oscillation parameters, such as a correlation between δCP and mνlightest.

Neutrino phenomenology and scalar Dark Matter with A4 flavor symmetry in Inverse and type II seesaw

We present a TeV scale seesaw mechanism for exploring the dark matter and neutrino phenomenology in the light of recent neutrino and cosmology data. A different realization of the Inverse seesaw (ISS) mechanism with A4 flavor symmetry is being implemented as a leading contribution to the light neutrino mass matrix which usually gives rise to vanishing reactor mixing angle θ13. Using a non-diagonal form of Dirac neutrino mass matrix and 3σ values of mass square differences we parameterize the neutrino mass matrix in terms of Dirac Yukawa coupling “y”. We then use type II seesaw as a perturbation which turns out to be active to have a non-vanishing reactor mixing angle without much disturbing the other neutrino oscillation parameters. Then we constrain a common parameter space satisfying the non-zero θ13, Yukawa coupling and the relic abundance of dark matter. Contributions of neutrinoless double beta decay are also included for standard as well as non-standard interaction. This study may have relevance in future neutrino and Dark Matter experiments.

On the CP Violation Phase in a Neutrino Mixing Model with an A4 Flavor Symmetry

Neutrino masses and mixing in an extended standard model acquiring an A4 flavour symmetry are considered. The corresponding three-neutrino mixing matrix obtained via a pertur- bative method allows us to determine the Dirac CP violation phase (\delta_{CP}) as a function of the mixing angles (\theta_{12}, \theta_{23}, \theta_{13}). Then, numerical values and distributions of \delta_{CP} are given. The latter values are quite close to the global fits of the experimental data for both the normal ordering and inverse ordering of the neutrino masses.

A predictive 3-3-1 model with A4 flavor symmetry

We propose a predictive model based on the SU(3)C⊗SU(3)L⊗U(1)X gauge group supplemented by the A4⊗Z3⊗Z4⊗Z6⊗Z16 discrete group, which successfully describes the SM fermion mass and mixing pattern. The small active neutrino masses are generated via inverse seesaw mechanism with three very light Majorana neutrinos. The observed charged fermion mass hierarchy and quark mixing pattern are originated from the breaking of the Z4⊗Z6⊗Z16 discrete group at very high scale. The obtained values for the physical observables for both quark and lepton sectors are in excellent agreement with the experimental data. The model predicts a vanishing leptonic Dirac CP violating phase as well as an effective Majorana neutrino mass parameter of neutrinoless double beta decay, with values mββ=2 and 48 meV for the normal and the inverted neutrino mass hierarchies, respectively.