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Register a new userNonzero |U_e3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle
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After the successful determination of the reactor neutrino mixing angle theta_13 ~ 0.16 eq 0, a new feature suggested by the current neutrino oscillation data is a sizeable deviation of the atmospheric neutrino mixing angle theta_23 from pi/4. Using the fact that the neutrino mixing matrix U = U_e^dagger U_ u, where U_e and U_ u result from the diagonalisation of the charged lepton and neutrino mass matrices, and assuming that U_ u has a i) bimaximal (BM), ii) tri-bimaximal (TBM) form, or else iii) corresponds to the conservation of the lepton charge L = L_e - L_mu - L_tau (LC), we investigate quantitatively what are the minimal forms of U_e, in terms of angles and phases it contains, that can provide the requisite corrections to U_ u so that theta_13, theta_23 and the solar neutrino mixing angle theta_12 have values compatible with the current data. Two possible orderings of the 12 and the 23 rotations in U_e, standard and inverse, are considered. The results we obtain depend strongly on the type of ordering. In the case of standard ordering, in particular, the Dirac CP violation phase delta, present in U, is predicted to have a value in a narrow interval around i) delta ~ pi in the BM (or LC) case, ii) delta ~ 3pi/2 or pi/2 in the TBM case, the CP conserving values delta = 0, pi, 2pi being excluded in the TBM case at more than 4sigma. In the addendum we discuss the implications of the latest 2013 data.
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We furnish a supersymmetric extension of the Standard Model with a flavour discrete symmetry $A_5$ under which the lepton fields transform as an irreducible triplet. Additional (`flavon) superfields are used to break $A_5$ into a $mathbb{Z}_2 times mathbb{Z}_2$ subgroup in the charged-lepton sector and another $mathbb{Z}_2$ subgroup in the neutrino sector. The first column of the resulting lepton mixing matrix is predicted and has entries which are related to the golden ratio. Using the observed $theta_{13}$ as input, our model predicts a solar mixing angle $theta_{12}$ in very good agreement with experiment; it also predicts a correlation between the atmospheric mixing angle $theta_{23}$ and the $CP$-violating Dirac phase $delta$.
We construct a class of renormalizable models for lepton mixing that generate predictions given in terms of the charged-lepton mass ratios. We show that one of those models leads, when one takes into account the known experimental values, to almost maximal CP-breaking phases and to almost maximal neutrinoless double-beta decay. We study in detail the scalar potential of the models, especially the bounds imposed by unitarity on the values of the quartic couplings.
A model independent analysis of the leptonic Dirac CP-violating phase ({delta}) is presented. The analysis uses the experimentally determined values of the mixing angles in the lepton mixing matrix in order to explore the allowed values for {delta} and possible general forms for the charged lepton mixing matrix. This is done under two general assumptions: 1) that the mixing matrix in the neutrino sector is the so-called tribimaximal matrix and hence the non zero value for {theta}13 arises due to the mixing matrix in the charged lepton sector and 2) the charged lepton mixing matrix is parametrized in terms of three angles and one phase. It is found that any value of {delta} is still consistent with the data and that, considering the assumptions above, regardless of the value for {delta}, the 1-3 mixing angle in the charged lepton sector is small but non zero and the 2-3 mixing angle can take values in only two possible small ranges around 0 and {pi}/2 respectively.
In terms of its eigenvector decomposition, the neutrino mass matrix (in the basis where the charged lepton mass matrix is diagonal) can be understood as originating from a tribimaximal dominant structure with small deviations, as demanded by data. If neutrino masses originate from at least two different mechanisms, referred to as hybrid neutrino masses, the experimentally observed structure naturally emerges provided one mechanism accounts for the dominant tribimaximal structure while the other is responsible for the deviations. We demonstrate the feasibility of this picture in a fairly model-independent way by using lepton-number-violating effective operators, whose structure we assume becomes dictated by an underlying $A_4$ flavor symmetry. We show that if a second mechanism is at work, the requirement of generating a reactor angle within its experimental range always fixes the solar and atmospheric angles in agreement with data, in contrast to the case where the deviations are induced by next-to-leading order effective operators. We prove this idea is viable by constructing an $A_4$-based ultraviolet completion, where the dominant tribimaximal structure arises from the type-I seesaw while the subleading contribution is determined by either type-II or type-III seesaw driven by a non-trivial $A_4$ singlet (minimal hybrid model). After finding general criteria, we identify all the $mathbb{Z}_N$ symmetries capable of producing such $A_4$-based minimal hybrid models.
The recent results from T2K and MINOS experiments point towards a relatively large value of the reactor angle theta_13 in the lepton sector. In this paper we show how a large theta_13 can arise from the charged lepton sector alone in the context of an SU(5) GUT. In such a scenario (tri-)bimaximal mixing in the neutrino sector is still a viable possibility. We also analyse the general implications of the considered scenario for the searches of CP violation in neutrino oscillations.
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