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Register a new userCobimaximal Neutrino Mixing from $A_4$ and its Possible Deviation
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It has recently been shown that the phenomenologically successful pattern of cobimaximal neutrino mixing ($theta_{13} eq 0$, $theta_{23} = pi/4$, and $delta_{CP} = pm pi/2$) may be achieved in the context of the non-Abelian discrete symmetry $A_4$, if the neutrino mass matrix is diagonalized by an orthogonal matrix ${cal O}$. We study how this pattern would deviate if ${cal O}$ is replaced by an unitary matrix.
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I propose a model of radiative charged-lepton and neutrino masses with $A_4$ symmetry. The soft breaking of $A_4$ to $Z_3$ lepton triality is accomplished by dimension-three terms. The breaking of $Z_3$ by dimension-two terms allow cobimaximal neutrino mixing $(theta_{13} eq 0, theta_{23} = pi/4, delta_{CP} = pm pi/2)$ to be realized with only very small finite calculable deviations from the residual lepton triality. This construction solves a long-standing technical problem inherent in renormalizable $A_4$ models since their inception.
It has recently been shown that the phenomenologically successful pattern of cobimaximal neutrino mixing ($theta_{13} eq 0$, $theta_{23} = pi/4$, and $delta_{CP} = pm pi/2$) may be achieved in the context of the non-Abelian discrete symmetry $A_4$. In this paper, the same goal is achieved with $S_3 times Z_2$. The residual lepton $Z_3$ triality in the case of $A_4$ is replaced here by $Z_2 times Z_2$. The associated phenomenology of the scalar sector is discussed.
We study the phenomenological implications of the modular symmetry $Gamma(3) simeq A_4$ of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus $tau$, which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with $A_4$ symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted $sin^2theta_{23}$ is restricted to be larger than $0.54$ and $delta_{CP}=pm (50^{circ}mbox{--}180^{circ})$. Since the correlation of $sin^2theta_{23}$ and $delta_{CP}$ is sharp, the prediction is testable in the future. It is remarkable that the effective mass $m_{ee}$ of the neutrinoless double beta decay is around $22$,meV while the sum of neutrino masses is predicted to be $145$,meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.
In the context of A_4 symmetry, neutrino tribimaximal mixing is achieved through the breaking of A_4 to Z_3 (Z_2) in the charged-lepton (neutrino) sector respectively. The implied vacuum misalignment of the (1,1,1) and (1,0,0) directions in A_4 space is a difficult technical problem, and cannot be treated without many auxiliary fields and symmetries (and perhaps extra dimensions). It is pointed out here that an alternative scenario exists with A_4 alone and no redundant fields, if neutrino masses are scotogenic, i.e. radiatively induced by dark scalar doublets as recently proposed.
We propose a simple framework based on $Delta(27)$ that leads to the successful cobimaximal lepton mixing ansatz, thus providing a predictive explanation for leptonic mixing observables. We explore first the effective neutrino mass operators, then present a specific model realization based on type I seesaw, and also propose a model with radiative 1-loop seesaw which features viable dark matter candidates.
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