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تسجيل مستخدم جديدSoft $A_4 to Z_3$ Symmetry Breaking and Cobimaximal Neutrino Mixing
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Ernest Ma
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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.
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اقرأ أيضاً
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.
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.
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 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.
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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