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Register a new userNon-diagonal charged lepton mass matrix, the TBM and non-zero $theta_{13}$
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Authors
Alma D. Rojas
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Assuming that the neutrino mass matrix is diagonalized by the TBM, we looked for the charged lepton mass matrix textures which render a lepton mixing matrix consistent with data. We were interested in the textures with the maximum number of zeros, so, we explored the cases of real matrices with three (and also four zeros) and found which of them provide solutions in agreement with data. We present the successful Yukawa textures and obtained the relative sizes of their non-zero entries. We found some interesting relations among the entries of these textures in terms of the charged lepton masses.
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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 $U_l$.
In this paper, we consider a neutrino mass model based on $A_4$ symmetry. The spontaneous symmetry breaking in this model is chosen to obtain tribimaximal mixing in the neutrino sector. We introduce $Z_2 times Z_2$ invariant perturbations in this model which can give rise to acceptable values of $theta_{13}$ and $delta_{CP}$. Perturbation in the charged lepton sector alone can lead to viable values of $theta_{13}$, but cannot generate $delta_{CP}$. Perturbation in the neutrino sector alone can lead to acceptable $theta_{13}$ and maximal CP violation. By adjusting the magnitudes of perturbations in both sectors, it is possible to obtain any value of $delta_{CP}$.
In this paper, we impose a magic symmetry on the neutrino mass matrix $M_{ u}$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Delta m_{i1}$, and the mixing angle $theta_{23}$. As new predictions, we obtain $sin theta_{12} = 0.584$ and $sin theta_{13} = 0.149$. The latter one is almost equal to the latest best fit.
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.
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.
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