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In this work we discuss the neutrino phenomenology in a $\Delta(54)$ discrete flavor symmetry and evaluate the relic abundance of dark matter (DM) and active neutrino-DM mixing angle considering various cosmological constraints. We introduced two Standard Model Higgs particles along with vector-like fermions and a new particle (S) which is a gauge singlet in the Standard Model. This modification leads to a mass matrix that diverges from the tribimaximal neutrino mixing pattern resulting in a non-zero reactor angle ($\theta_{13}$). We also incorporated a $ Z_2 \otimes Z_3 \otimes Z_4$ symmetry for the specific interactions in our model. The additional particle S is a sterile neutrino which is considered to be a probable dark matter candidate with mass in keV range., Comment: 13 pages, 6 figures, 2 tables

The current work involves augmenting the $\Delta(54)$ discrete flavor model by incorporating two Standard Model Higgs particles into the Inverse Seesaw mechanism. We introduced Weyl fermions and Vector like fermions, which are gauge singlets in the Standard Model and produces Majorana mass terms in our lagrangian. The resulting mass matrix deviates from the tribimaximal neutrino mixing pattern producing a non-zero reactor angle ($\theta_{13}$) . We have determined the effective Majorana neutrino mass, which is the parameter of relevance in neutrinoless double beta decay investigations, using the model's limited six-dimensional parameter space. We additionally investigate the possibility of baryogenesis in the proposed framework via resonant leptogenesis. We have the non-zero value for resonantly enhanced CP asymmetry originating from the decay of right-handed neutrinos at the TeV scale, accounting for flavor effects. The evolution of lepton asymmetry is systematically analyzed by numerically solving a set of Boltzmann equations, leading to the determination of the baryon asymmetry with a magnitude of $ \lvert \eta_B \rvert \approx 6 \times 10^{-10}$. This outcome is achieved by selecting specific values for the right-handed neutrino mass $M_1 = 10$ TeV and mass splitting, $d \approx 10^{-8}$., Comment: 13 pages, 5 figures, 2 tables

The present study entails the augmentation of the $\Delta$(54) flavor symmetry model by including the ISS mechanism by two Standard Model Higgs particles, achieved by the inclusion of different flavons. The matrices are discussed numerically in the framework of the $\Delta(54)$ flavor model with the ISS mechanism for Majorana neutrinos. We introduced Vector like (VL) fermions and a Weyl fermion, which are gauge singlets in the Standard Model. We restrict the undesirable terms in our Lagrangian using additional symmetry. Due to the addition of additional flavons, the precise tribimaximal neutrino mixing pattern deviates, resulting in the creation of a non-zero reactor angle $\theta_{13}$. We found that the atmospheric oscillation parameter ($\theta_{23}$) occupies the upper octant under the normal hierarchy situation. We also study the CP violation ($\delta_{CP}$) , Jarlskog invariant parameter ($J$), and Neutrinoless double-beta decay parameter ($m_{ee}$) in the parameter space of the normal hierarchy model to see whether they accord with the most recent neutrino observations., Comment: 17 pages, 5 figures, 2 tables

We study a neutrino mass model with $A_4$ discrete flavor symmetry using a type-I seesaw mechanism. The inclusion of extra flavons in our model leads to the deviations from exact tribimaximal mixing pattern resulting in a nonzero $\theta_{13}$ consistent with the recent experimental results and a sum rule for light neutrino masses is also obtained. In this framework, a connection is established among the neutrino mixing angles: reactor mixing angle($\theta_{13}$), solar mixing angle($\theta_{12}$) and atmospheric mixing angle ($\theta_{23}$). This model also allows us a prediction of Dirac CP-phase and Jarlskog parameter $J$. The octant of the atmospheric mixing angle $\theta_{23}$ occupies the lower octant. Our model prefers normal hierarchy (NH) than inverted hierarchy (IH). We use the parameter space of our model of neutrino masses to study the neutrinoless double beta decay parameter $m_{ee}$. Keywords: Discrete flavor symmetry, Type-I seesaw mechanism, Tribimaximal mixing, Dirac CP-phase, Jarlskog parameter, Neutrinoless double beta decay, Comment: 15 pages, 3 Figures, 2 Tables. arXiv admin note: substantial text overlap with arXiv:2203.05536

Our analysis involves enhancing the $\Delta(54)$ flavor symmetry model with Inverse Seesaw mechanism along with two SM Higgs through the incorporation of distinct flavons. Additionally, we introduce supplementary $Z_2\otimes Z_3 \otimes Z_4$ symmetries to eliminate any undesirable components within our investigation. The exact tri-bimaximal neutrino mixing pattern undergoes a deviation as a result of the incorporation of extra flavons, leading to the emergence of a non-zero reactor angle $\theta_{13}$ that aligns with the latest experimental findings. It was found that for our model the atmospheric oscillation parameter occupies the lower octant for normal hierarchy case. We also examine the parameter space of the model for normal hierarchy to explore the Dirac CP ($\delta_{CP}$), Jarlskog invariant parameter ($J$) and the Neutrinoless double-beta decay parameter ($m_{\beta\beta}$) and found it in agreement with the neutrino latest data. Hence our model may be testable in the future neutrino experiments., Comment: 18 pages, 6 figures, 3 tables