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Register a new userLepton flavor models with discrete prediction of theta_{13}
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We study the lepton flavor models with the flavor symmetry (Z_N times Z_N times Z_N)rtimes Z_3. Our models predict non-vanishing discrete values of theta_{13} as well as theta_{12} and theta_{23} depending on N. For certain values, our models realize the tri-bimaximal mixing angles with theta_{13}=0. For other values, our models provide with discrete deviation from the tri-bimaximal mixing angles.
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We present the correlation of low energy CP phases, both Dirac and Majorana, and the lepton asymmetry for the baryon asymmetry in the universe, with a certain class of Yukawa matrices that consist of two right-handed neutrinos and include one texture zero in themselves. For cases in which the amount of the lepton asymmetry $Y_L$ turns out to be proportional to $theta_{13}^2$, we consider the relation between two types of CP phases and the relation of $Y_L$ versus the Jarlskog invariant or the amplitude of neutrinoless double beta decay as $theta_{13}$ varies.
Renormalization group (RG) evolution of the neutrino mass matrix may take the value of the mixing angle $theta_{13}$ very close to zero, or make it vanish. On the other hand, starting from $theta_{13}=0$ at the high scale it may be possible to generate a non-zero $theta_{13}$ radiatively. In the most general scenario with non-vanishing CP violating Dirac and Majorana phases, we explore the evolution in the vicinity of $theta_{13}=0$, in terms of its structure in the complex ${cal U}_{e3}$ plane. This allows us to explain the apparent singularity in the evolution of the Dirac CP phase $delta$ at $theta_{13}=0$. We also introduce a formalism for calculating the RG evolution of neutrino parameters that uses the Jarlskog invariant and naturally avoids this singular behaviour. We find that the parameters need to be extremely fine-tuned in order to get exactly vanishing $theta_{13}$ during evolution. For the class of neutrino mass models with $theta_{13}=0$ at the high scale, we calculate the extent to which RG evolution can generate a nonzero $theta_{13}$, when the low energy effective theory is the standard model or its minimal supersymmetric extension. We find correlated constraints on $theta_{13}$, the lightest neutrino mass $m_0$, the effective Majorana mass $m_{ee}$ measured in the neutrinoless double beta decay, and the supersymmetric parameter $tanbeta$.
Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting relations among the entries of these textures in terms of the charged lepton masses. We also show that these relations can be obtained directly from a parametrization of the charged lepton mixing matrix $U_l$.
Solar neutrino experiments have yet to see directly the transition region between matter-enhanced and vacuum oscillations. The transition region is particularly sensitive to models of non-standard neutrino interactions and propagation. We examine several such non-standard models, which predict a lower-energy transition region and a flatter survival probability for the ^{8}B solar neutrinos than the standard large-mixing angle (LMA) model. We find that while some of the non-standard models provide a better fit to the solar neutrino data set, the large measured value of theta_{13} and the size of the experimental uncertainties lead to a low statistical significance for these fits. We have also examined whether simple changes to the solar density profile can lead to a flatter ^{8}B survival probability than the LMA prediction, but find that this is not the case for reasonable changes. We conclude that the data in this critical region is still too poor to determine whether any of these models, or LMA, is the best description of the data.
By postulating the relation theta_{23} simeq 45^circ + etatheta_{13}, we seek preferable correction terms to tri-bi-maximal mixing and discuss their origins. Global analyses of the neutrino oscillation parameters favor eta=pm 1/sqrt{2}; this corresponds to the relation found by Edy, Frampton, and Matsuzaki some years ago in the context of a T^prime flavor symmetry. In contrast, the results of the u_mu disappearance mode reported by the T2K and Super-Kamiokande collaborations seem to prefer eta=0, which gives an almost maximal theta_{23}. We derive a general condition for ensuring theta_{23} simeq 45^circ + etatheta_{13} and find that the condition is complicated by the neutrino masses and CP violating phases. We investigate the condition under simplified environments and arrive at several correction terms to the mass matrices. It is found that the obtained correction terms can arise from flavor symmetries or one-loop radiative corrections.
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