We study a flavor model that the quark sector has $S_3$ modular symmetry,while lepton $A_4$ symmetry. Our leads to characteristic mass matrices which are consistent with experimental data of masses, mixing angles and CP violating phase. The is also neutrino oscillations. baryon number violations in our model.

A bstract We study a flavor model with 4 symmetry which originates from S modular group. In symmetry, Z 2 subgroup can be anomalous, and then violated to . Starting symmetric Lagrangian at the tree level, quantum level has only when in is anomalous. obtain forms of two singlets triplet representations by decomposing into representations. propose new leptons using those forms. succeed constructing viable neutrino mass matrix through Weinberg operator for both normal hierarchy (NH) inverted...

A bstract We study the phenomenological implications of modular symmetry Γ(3) ≃ 4 lepton flavors facing recent experimental data neutrino oscillations. The mass matrices neutrinos and charged leptons are essentially given by fixing expectation value modulus τ , which is only source invariance breaking. introduce no flavons in contrast with conventional flavor models symmetry. classify our along type I seesaw model, Weinberg operator model Dirac model. In normal hierarchy masses, available...

We study the modulus stabilization in an $A_4$ model whose flavor symmetry is originated from $S_4$ modular symmetry. can stabilize so that invariant superpotential leads to realistic lepton masses and mixing angles. also discuss phenomenological aspect of present as a consequence stabilization.

We study the spontaneous $CP$ violation through stabilization of modulus $\tau$ in modular invariant flavor models. The $CP$-invaraiant potentential has minimum only at ${\rm Re}[\tau] = 0$ or 1/2. From this prediction, we physical phase is vanishing. important point for conservation $T$ transformation symmetry. One needs symmetry to realize violation.

We present a flavor model with the $S_3$ modular invariance in framework of SU(5) GUT. The forms weights $2$ and $4$ give quark lepton mass matrices common complex parameter, modulus $τ$. GUT relation down-type quarks charged leptons is imposed by VEV adjoint 24-dimensional Higgs multiplet addition to VEVs $5$ $\bar 5$ multiples SU(5). observed CKM PMNS mixing parameters as well eigenvalues are reproduced properly. discuss leptonic CP phase effective neutrinoless double beta decay sum...

We revisit the $A_4$ model for leptons in light of new result NuFIT 3.2. introduce a flavon $η$ transforming as singlet $1'$ or $1"$ which couples to both charged and neutrinos next-leading order operators. The consists five parameters: lightest neutrino mass $m_1$, vacuum expectation value three CP violating phases after inputting experimental values $Δm_{\rm atm}^2$ sol}^2$. with gives prediction $\sin^2 θ_{12}$ around best fit 3.2 while keeping near maximal mixing $θ_{23}$. Inputting...

We study the minimal seesaw model, where two right-handed Majorana neutrinos are introduced, focusing on CP violating phase. In addition, we take trimaximal mixing pattern for neutrino flavor charged lepton mass matrix is diagonal. Thanks to this symmetric framework, $3\times 2$ Dirac given in terms of a few parameters. Numerical studies reveal that observation phase can determine structure model. particular, new matrices proposed case $\rm TM_1$, which derived by additional 2-3 family...

We discuss the correlation between CP violating Dirac phase of lepton mixing matrix and cosmological baryon asymmetry based on leptogenesis in minimal seesaw model with two right-handed Majorana neutrinos trimaximal for neutrino flavors. The sign at low energy is fixed by observed since there only one parameter model. According to recent T2K NOνA data violation, mass our normal hierarchy masses.

We discuss a supersymmetric model with discrete flavor symmetry . The additional scalar fields which contribute masses of leptons in the Yukawa terms are introduced this model. analyze their potential and find that they have various vacuum structures. show relations among 24 different vacua classify them into two types. derive expressions lepton mixing angles, Dirac CP violating phase Majorana phases for parameters allowed by experimental data angles each type. also study constraints on...

We discuss the relation between CP violation of quark mixing and that lepton by investigating a violating observable, Jarlskog invariant, as well Dirac phase. The down-type mass matrix with three zeros is given in terms minimal number parameters, while up-type diagonal. These matrices leading to successful CKM angles are embedded both Pati--Salam SU(5) models. leptonic invariant $J_{CP}^l$ (as phase) examined for two cases: neutrino diagonal or non-diagonal, where no additional phase...

Abstract The type-I seesaw model is a common extension to the Standard Model that describes neutrino masses. introduces heavy right-handed neutrinos with Majorana mass transform as electroweak gauge singlets. We initially study case two called 3-2 model. At an energy scale above neutrinos, effective matrix rank degenerate, implying lightest massless. After considering renormalization effects below remains degenerate. Next, we three 3-3 Above of construct be solving for energies find depends...

We discuss the minimal seesaw model for Dirac CP violating phase of lepton mixing matrix. introduce two right-handed Majorana neutrinos and obtain several textures tri-maximal matrices. Moreover, we observed baryon asymmetry universe through leptogenesis mechanism. As result, specific which predicts negative sign maximal normal hierarchy neutrino masses.

We propose a model with $A_4$ flavor symmetry for leptons and quarks in the framework of supersymmetric SU(5) grand unified theory (GUT). The running masses charged at GUT scale ($\sim 10^{16}$ GeV) are realized by adjoint 24-dimensional Higgs multiplet additional gauge singlet scalar fields including flavons. In this paper, we focus on result quark lepton mixing since our present is known to reproduce recent experimental results neutrino mass oscillation. Those showed numerically.