We make an investigation of modular $Γ^{\prime}_5 \simeq A^{\prime}_5$ group in inverse seesaw framework. Modular symmetry is advantageous because it reduces the usage of extra scalar fields significantly. Moreover, the Yukawa couplings are expressed in terms of Dedekind eta functions, which also have a $q$ expansion form, utilized to achieve numerical simplicity. Our proposed model includes six heavy fermion superfields i.e., $\mathcal{N}_{Ri}$, $\mathcal{S}_{Li}$ and a weighton. The study of neutrino phenomenology becomes simplified and effective by the usage of $A^\prime_5$ modular symmetry, which provides us a well defined mass structure for the lepton sector. Here, we observe that all the neutrino oscillation parameters, as well as the effective electron neutrino mass in neutrinoless double beta decay can be accommodated in this model. We also briefly discuss the lepton flavor violating decays $\ell_i \to \ell_j γ$ and comment on non-unitarity of lepton mixing matrix.
We propose a supersymmetric radiative seesaw model with modular $A_4$ symmetry. Thanks to contributions of supersymmetric partners to one-loop diagrams generating neutrino masses, we successfully fit neutrino data and obtain predictions in case of normal hierarchy in a minimal framework that would not be realized in a non-supersymmetric model. We show a several predictive figures and demonstrate a best fit benchmark point through $χ^2$
We discuss an inverse seesaw model based on right-handed fermion specific $U(1)$ gauge symmetry and $A_4$-modular symmetry. These symmetries forbid unnecessary terms and restrict structures of Yukawa interactions which are relevant to inverse seesaw mechanism. Then we can obtain some predictions in neutrino sector such as Dirac-CP phase and sum of neutrino mass, which are shown by our numerical analysis. Besides the relation among masses of heavy pseudo-Dirac neutrino can be obtained since it is also restricted by the modular symmetry. We also discuss implications to lepton flavor violation an…
We study one-loop induced radiative seesaw model applying a modular $A_4$ flavor symmetry, in which the neutrino mass matrix is achieved by two different Yukawa couplings one of which also contributes to positive value of muon anomalous magnetic moment as well as lepton flavor violations. Thanks to the specific mass matrix via $A_4$ symmetry and its modular weight, we find several predictions for lepton sector through our numerical analysis.
We discuss a linear seesaw model with local $U(1)_{B-L}$ and modular $A_4$ symmetries. The neutrino mass matrix for linear seesaw mechanism is realized by $U(1)_{B-L}$ charge assignment and the nature of modular $A_4$ symmetry. We formulate neutrino mass and carry our numerical analysis showing some predictions for observables in neutrino sector. Remarkably, the case of inverted neutrino mass ordering (IO) is realized by a specific region around $τ=ω=e^{2πi/3}$, which is favored by a string theory. Thus, our prediction would be very strong in case of IO.
We propose a one-loop induced radiative seesaw model applying a modular $S_3$ flavor symmetry, which is known as the minimal non-Abelian discrete group. In this scenario, dark matter (DM) candidate is correlated with neutrinos and lepton flavor violations (LFVs). We show several predictions of mixings and phases satisfying LFVs, observed relic density, and neutrino oscillation data.
We propose a radiative seesaw model based on a modular $A_4$ symmetry, which has good predictability in the lepton sector. We execute a numerical analysis to search for parameters that satisfy the experimental constraints such as those from neutrino oscillation data and lepton flavor violations. Then, we present several predictions in our model that originate from the modular symmetry at a fixed point as well as fundamental region of $τ$.
We discuss a linear seesaw model with as minimum field content as possible, introducing a modular $S_4$ with the help of gauged $U(1)_{B-L}$ symmetries. Due to rank two neutrino mass matrix, we have a vanishing neutrino mass eigenvalue, and only the normal mass hierarchy of neutrinos is favored through the modular $S_4$ symmetry. In our numerical $Δχ^2$ analysis, we especially find rather sharp prediction on sum of neutrino masses to be around $60$ meV in addition to the other predictions.
We propose an inverse seesaw model with large $SU(2)_L$ multiplets applying modular $A_4$ symmetry where $SU(2)_L$ quartet and septet fermions are introduced as triplets under the symmetry. The neutral components of the quartet contribute to mass matrix for inverse seesaw mechanism and interactions involving the septet induce Majorana mass terms of these extra fermions. Although there are several free parameters in the mass matrix we can obtain some predictions for observables in neutrino sector such as CP phases, sum of neutrino mass and effective mass for neutrinoless double beta decay, espe…
We make an attempt to study neutrino phenomenology in the framework of type-III seesaw by considering $A_4$ modular symmetry in the super-symmetric context. In addition, we have included a local $U(1)_{B-L}$ symmetry which eventually helps us to avoid certain unwanted terms in the superpotential. Hitherto, the seesaw being type-III, it involves three fermion triplet superfields $Σ_R$, along with which, we have included a singlet weighton field $(ρ)$. In here, modular symmetry plays a crucial role by avoiding the usage of excess flavon (weighton) fields. Also, the Yukawa couplings acquire modul…
In this paper, we incorporate the modular $S^{}_4$ flavor symmetry into the supersymmetric version of the minimal type-I seesaw model, in which only two right-handed neutrino singlets are introduced to account for tiny Majorana neutrino masses, and explore its implications for the lepton mass spectra, flavor mixing and CP violation. The basic idea is to assign two right-handed neutrino singlets into the unique two-dimensional irreducible representation of the modular $S^{}_4$ symmetry group. Moreover, we show that the matter-antimatter asymmetry in our Universe can be successfully explained vi…
The present work is inspired by the application of $A_4$ modular symmetry in the linear seesaw framework, which restricts the use of multiple flavon fields. Linear seesaw is realized with six heavy $SU(2)_L$ singlet fermion superfields and a weighton in a supersymmetric framework. The non-trivial transformation of Yukawa couplings under the $A_4$ modular symmetry helps to explore the neutrino phenomenology with a specific flavor structure of the mass matrix. We discuss the phenomena of neutrino mixing and show that the obtained mixing angles and CP violating phase in this framework are compati…
In this paper, we investigate the implication of modular $Γ^{\prime}_5 \simeq A^{\prime}_5$ symmetry on neutrino oscillation phenomenology in the linear seesaw framework. In order to achieve the well defined mass structure for the light active neutrinos as dictated by the linear seesaw mechanism, we introduce six heavy fermion fields along with a pair of weightons to retain the holomorphic nature of the superpotential. The notable feature of modular symmetry is that, it reduces the usage of flavon fields significantly. In addition, the Yukawa couplings transform non-trivially under the flavor …
Discrete symmetries being preferred to explain the neutrino phenomenology, we chose the simplest $S_3$ group and explore the implication of its modular form on neutrino masses and mixing. Non-trivial transformations of Yukawa couplings under this symmetry, make the model phenomenologically interesting by reducing the requirement of multiple scalar fields. This symmetry imposes a specific flavor structure to the neutrino mass matrix within the framework of less frequented type III seesaw mechanism and helps to explore the neutrino mixing consistent with the current observation. Apart, we also e…
We discuss type-II seesaw models adopting modular $A_4$ symmetry in supersymmetric framework. In our approach, the models are classified by the assignment of $A_4$ representations and modular weights for leptons and triplet Higgs fields. Then neutrino mass matrix is characterized by modulus $τ$ and two free parameters. Carrying out numerical analysis, we find allowed parameter sets which can fit the neutrino oscillation data. For the allowed parameter sets, we obtain the predictions in neutrino sector such as CP violating phases and the lightest neutrino mass. Finally we also show the predicti…
In this paper, we investigate the double covering of modular $Γ^{}_5 \simeq A^{}_5$ group and derive all the modular forms of weight one for the first time. The modular forms of higher weights are also explicitly given by decomposing the direct products of weight-one forms. For the double covering group $Γ^\prime_5 \simeq A^\prime_5$, there exist two inequivalent two-dimensional irreducible representations, into which we can assign two right-handed neutrino singlets in the minimal seesaw model. Two concrete models with such a salient feature have been constructed to successfully explain lepton…
We present the first complete model of the Littlest Modular Seesaw, based on two right-handed neutrinos, within the framework of multiple modular symmetries, justifying the use of multiple moduli fields which take their values at 3 specific stabilizers of $Γ_4 \simeq S_4$, including a new phenomenological possibility. Using a semi-analytical approach, we perform a $χ^2$ analysis of each case and show that good agreement with neutrino oscillation data is obtained, including predictive relations between the leptonic mixing angles and the ratio of light neutrino masses, which non-trivially agree …
In this paper, we study the implications of the modular $A^{}_4$ 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. The right-handed neutrino as well as the Higgs triplets in this model are assigned into the trivial one-dimensional irreducible representation of the modular group $A^{}_{4}$. We show that the individual contributions to the neutrino masses from the right-handed neutrino and the Higgs triplet are com…
We study a double covering of modular $A_4$ flavor symmetry in which we construct lepton models in cases of canonical seesaw and radiative seesaw models. Through $χ$ square numerical analysis, we show some predictions for the cases, depending on normal and inverted hierarchies.
Assuming the existence of an eV or KeV scale sterile neutrino, we develop a 3+1 neutrino mass model using $A_4\times Z_4 \times Z_2$ symmetry group. Three Higgs $H, H^{\prime}$ and $H^{\prime\prime}$ are considered to give a desired neutrino mass matrix which generates non-zero $θ_{13}$. The model can give neutrino mixing parameters that are well within the experimental 3$σ$ bounds. We also calculate the $4\times 4$ active-sterile neutrino mixing matrix, and it is found to be consistent with experimental bounds.
The topological classification of one-loop Weinberg operator at dimension-5 leads to systematic categorization of one-loop neutrino mass models. All one-loop neutrino mass models must fall in one of these categories. Among these topological categories, loop extension of canonical seesaw scenarios is interesting in light of the current LHC run. Apart from one-loop contribution, these extensions result in dominant tree-level contribution to neutrino masses. The immediate remedy to obtain dominant one-loop contribution requires combination of flavor symmetries and enlarged field content. Alternat…
We consider a class of gauged $U(1)$ extensions of the Standard Model (SM), where the light neutrino masses are generated by an inverse seesaw mechanism. In addition to the three right handed neutrinos, we add three singlet fermions and demand an extra $Z_2$ symmetry under which, the third generations of both of the neutral fermions are odd, which in turn gives us a stable dark matter candidate. We express the $U(1)$ charges of all the fermions in terms of the U(1) charges of the standard model Higgs and the new complex scalar. We study the bounds on the parameters of the model from vacuum sta…
In this paper, we present a systematic investigation on simple inverse seesaw models for neutrino masses and flavor mixing based on the modular $S^{}_4$ symmetry. Two right-handed neutrinos and three extra fermion singlets are introduced to account for light neutrino masses through the inverse seesaw mechanism, and to provide a keV-mass sterile neutrino as the candidate for warm dark matter in our Universe. Considering all possible modular forms with weights no larger than four, we obtain twelve models, among which we find one is in excellent agreement with the observed lepton mass spectra and…
We study Flipped $SU(5)\times U(1)$ Grand Unified Theories (GUTs) with $Γ_3\simeq A_4$ modular symmetry. We propose two models with different modular weights assignments, where the fermion mass hierarchy can arise from weighton fields. In order to relax the constraint on the Dirac neutrino Yukawa matrix we appeal to mechanisms which allow incomplete GUT representations, allowing a good fit to quark and charged lepton masses and quark mixing for a single modulus field $τ$, with the neutrino masses and lepton mixing well determined by the type I seesaw mechanism, at the expense of some tuning. W…
