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Register a new userCP violations in a predictive $A_4$ symmetry model
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We will investigate numerically a seesaw model with $A_4$ flavor symmetry to find allowed regions satisfying the current experimental neutrino oscillation data, then use them to predict physical consequences. Namely, the lightest active neutrino mass has order of $mathcal{O}(10^{-2})$ eV. The effective neutrino mass $|langle mrangle|$ associated with neutrinoless double beta decay is in the range of $[0.002 ;mathrm{eV},0.038;mathrm{eV}]$ and $[0.048;mathrm{eV},0.058;mathrm{eV}]$ corresponding to the normal and the inverted hierarchy schemes. Other relations among relevant physical quantities are shown, so that they can be determined if some of them are confirmed experimentally. The recent data of the baryon asymmetry of the Universe ($eta_B$) can be explained via leptogenesis caused by the effect of the renormalization group evolution on the Dirac Yukawa couplings, provided the right handed neutrino mass scale $M_0$ is ranging from $mathcal{O}(10^8)$ GeV to $mathcal{O}(10^{12})$ GeV for $tanbeta =3$. This allowed $M_0$ range distinguishes with the scale of $mathcal{O}(10^{13})$ GeV concerned by other effects that also generate the consistent $eta_B$ from leptogenesis. The branching ratio of the decay $ mu rightarrow,egamma$ may reach the future experimental sensitivity in the very light values of $M_0$. Hence, it will be inconsistent with the $M_0$ range predicted from the $eta_B$ data whenever this decay is detected experimentally.
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In this paper, we consider a neutrino mass model based on $A_4$ symmetry. The spontaneous symmetry breaking in this model is chosen to obtain tribimaximal mixing in the neutrino sector. We introduce $Z_2 times Z_2$ invariant perturbations in this model which can give rise to acceptable values of $theta_{13}$ and $delta_{CP}$. Perturbation in the charged lepton sector alone can lead to viable values of $theta_{13}$, but cannot generate $delta_{CP}$. Perturbation in the neutrino sector alone can lead to acceptable $theta_{13}$ and maximal CP violation. By adjusting the magnitudes of perturbations in both sectors, it is possible to obtain any value of $delta_{CP}$.
We worked out in detail the three-Higgs-doublet extension of the standard model when the $A_4$ symmetry, which is imposed to solve the flavor problem, is extended to the scalar sector. The three doublets may be related to the fermion mass generation and, in particular, they may be the unique responsible for the generation of the neutrino masses. If this is the case, the respective VEVs have to be quite smaller than the electroweak scale if no fine tuning in the Yukawa couplings is assumed. We consider here the mass spectra in the scalar sector in three different situations. In one of them there are no light scalars at all, but in the other ones a light or two massless scalars, at the tree level, may survive. The later fields are safe, from the phenomenological point of view, since it couples mainly with neutrinos and/or becomes enough massive at the tree level if there exist trilinear interactions. Quantum effects may be important too.
In a recently proposed multi-Higgs extension of the standard model in which discrete symmetries, $A_4$ and $Z_3$ are imposed we show that, after accommodating the fermion masses and the mixing matrices in the charged currents, the mixing matrices in the neutral currents induced by neutral scalars are numerically obtained. However, the flavor changing neutral currents are under control mainly by mixing and/or mass suppressions in the neutral scalar sector.
The Zee model generates neutrino masses at the one-loop level by adding charged SU(2)_L-singlet and extra SU(2)_L-doublet scalars to the standard model of particle physics. As the origin of the nontrivial structure of the lepton flavor mixing, we introduce the softly broken A_4 symmetry to the Zee model. This model is compatible with the tribimaximal mixing which agrees well with neutrino oscillation measurements. Then, a sum rule m_1 e^{i alpha_12} + 2 m_2 + 3 m_3 e^{i alpha_32} = 0 is obtained and it results in Delta m^2_31 < 0 and m_3 > 1.8*10^{-2}eV. The effective mass |(M_nu)_{ee}| for the neutrinoless double beta decay is predicted as | (M_ u)_{ee} | > 1.7*10^{-2}eV. The characteristic particles in this model are SU(2)_L-singlet charged Higgs bosons s^+_alpha (alpha=xi,eta,zeta) which are made from a 3-representation of A_4. Contributions of s^+_alpha to the lepton flavor violating decays of charged leptons are almost forbidden by an approximately remaining Z_3 symmetry; only BR(tau to ebar mu mu) can be sizable by the flavor changing neutral current interaction with SU(2)_L-doublet scalars. Therefore, s^+_alpha can be easily light enough to be discovered at the LHC with satisfying current constraints. The flavor structures of BR(s^-_alpha to ell nu) are also discussed.
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 and collider physics in our model.
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