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Register a new userCobimaximal Neutrino Mixing from $S_3 times Z_2$
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Authors
Ernest Ma
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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 $A_4$. 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.
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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.
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.
Cobimaximal lepton mixing, i.e. $theta_{23} = 45^circ$ and $delta = pm 90^circ$ in the lepton mixing matrix $V$, arises as a consequence of $S V = V^ast mathcal{P}$, where $S$ is the permutation matrix that interchanges the second and third rows of $V$ and $mathcal{P}$ is a diagonal matrix of phase factors. We prove that any such $V$ may be written in the form $V = U R P$, where $U$ is any predefined unitary matrix satisfying $S U = U^ast$, $R$ is an orthogonal, i.e. real, matrix, and $P$ is a diagonal matrix satisfying $P^2 = mathcal{P}$. Using this theorem, we demonstrate the equivalence of two ways of constructing models for cobimaximal mixing---one way that uses a standard $CP$ symmetry and a different way that uses a $CP$ symmetry including $mu$--$tau$ interchange. We also present two simple seesaw models to illustrate this equivalence; those models have, in addition to the $CP$ symmetry, flavour symmetries broken softly by the Majorana mass terms of the right-handed neutrino singlets. Since each of the two models needs four scalar doublets, we investigate how to accommodate the Standard Model Higgs particle in them.
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.
If neutrinos are Dirac, the conditions for cobimaximal mixing, i.e. $theta_{23}=pi/4$ and $delta_{CP}=pm pi/2$ in the $3 times 3$ neutrino mixing matrix, are derived. One example with $A_4$ symmetry and radiative Dirac neutrino masses is presented.
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