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Register a new userExtended scaling and residual flavor symmetry in the neutrino Majorana mass matrix
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The residual symmetry approach, along with a complex extension for some flavor invariance, is a powerful tool to uncover the flavor structure of the $3times3$ neutrino Majorana mass matrix $M_ u$ towards gaining insights into neutrino mixing. We utilize this to propose a complex extension of the real scaling ansatz for $M_ u$ which was introduced some years ago. Unlike the latter, our proposal allows a nonzero mass for each of the three light neutrinos as well as a nonvanishing $theta_{13}$. A major result of this scheme is that leptonic Dirac CP-violation must be maximal while atmospheric neutrino mixing need not be exactly maximal. Moreover, each of the two allowed Majorana phases, to be probed by the search for nuclear $0 u betabeta$ decay, has to be at one of its two CP-conserving values. There are other interesting consequences such as the allowed occurrence of a normal mass ordering which is not favored by the real scaling ansatz. Our predictions will be tested in ongoing and future neutrino oscillation experiments at T2K, NO$ u$A and DUNE.
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Using the residual symmetry approach, we propose a complex extension of the scaling ansatz on $M_ u$ which allows a nonzero mass for each of the three light neutrinos as well as a nonvanishing $theta_{13}$. Leptonic Dirac CP violation must be maximal while atmospheric neutrino mixing need not to be exactly maximal. Each of the two Majorana phases, to be probed by the search for $0 u betabeta$ decay, has to be zero or $pi$ and a normal neutrino mass hierarchy is allowed.
The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an intuitive display of the structure of the Majorana neutrino mass matrix, using the whole set of the oscillation data. The structure is revealed depending on the lightest neutrino mass. We find that there are three regions with distinct characteristics of structure. A group effect and the $mu$-$tau$ exchange symmetry are observed. Six types of texture non-zeros are shown. Implications for flavor models are discussed.
We investigate the Majorana neutrino mass matrix $M_{ u}$ with one parameter in the context of two texture zeros and its symmetry realization by non-Abelian discrete symmetry. From numerical calculation, we confirm that the textures $(M_{ u})_{11,12}=0$ and $(M_{ u})_{11,13}=0$ are consistent with the current experimental constraints, and show the correlations between non-zero elements of $M_{ u}$. The ratios of non-zero elements of $M_{ u}$ are constrain in small regions, and we find simple examples of $M_{ u}$ with one real mass parameter. We also discuss symmetry realization of the mass matrix by the type-II seesaw mechanism based on the binary icosahedral symmetry $A_5$ .
A new idea for neutrino mass was proposed recently, where its smallness is not due to the seesaw mechanism, i.e. not inversely proportional to some large mass scale. It comes from a one-loop mechanism with dark matter in the loop consisting of singlet Majorana fermions $N_i$ with masses of order 10 keV and neutrino masses are scaled down from them by factors of about $10^{-5}$. We discuss how this model may be implemented with the non-Abelian discrete symmetry $A_4$ for neutrino mixing, and consider the phenomenology of $N_i$ as well as the extra scalar doublet $(eta^+,eta^0)$.
The $mu$-$tau$ exchange symmetry in the neutrino mass matrix and its breaking as a perturbation are discussed. The exact $mu$-$tau$ symmetry restricts the 2-3 and 1-3 neutrino mixing angles as $theta_{23} = pi/4$ and $theta_{13} = 0$ at a zeroth order level. We claim that the $mu$-$tau$ symmetry breaking prefers a large CP violation to realize the observed value of $theta_{13}$ and to keep $theta_{23}$ nearly maximal, though an artificial choice of the $mu$-$tau$ breaking can tune $theta_{23}$, irrespective of the CP phase. We exhibit several relations among the deviation of $theta_{23}$ from $pi/4$, $theta_{13}$ and Dirac CP phase $delta$, which are useful to test the $mu$-$tau$ breaking models in the near future experiments. We also propose a concrete model to break the $mu$-$tau$ exchange symmetry spontaneously and its breaking is mediated by the gauge interactions radiatively in the framework of the extended gauge model with $B-L$ and $L_mu - L_tau$ symmetries. As a result of the gauge mediated $mu$-$tau$ breaking in the neutrino mass matrix, the artificial choice is unlikely, and a large Dirac CP phase is preferable.
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