Many unified models predict two large neutrino mixing angles, with the charged lepton mixing angles being small and quark-like, and the neutrino masses being hierarchical. Assuming this, we present simple approximate analytic formulae giving the lepton mixing angles in terms of the underlying high energy neutrino mixing angles together with small perturbations due to both charged lepton corrections and renormalisation group (RG) effects, including also the effects of third family canonical normalization (CN). We apply the perturbative formulae to the ubiquitous case of tri-bimaximal neutrino mixing at the unification scale, in order to predict the theoretical corrections to mixing angle predictions and sum rule relations, and give a general discussion of all limiting cases.
We parametrize lepton mixing matrix, known as PMNS matrix, in terms of three parameters which account deviations of three mixing angles from their bi-maximal or tri-bimaximal values. On the basis of this parametrization we can determine corresponding charged lepton mixing matrix in terms of those three parameters which can deviate bi-maximal or tri-bimaximal mixing. We find that the charged lepton mixing matrices which can deviate bi-maximal mixing matrix and tri-bimaximal mixing matrix exhibit similar structures. Numerical analysis shows that these charged lepton mixing matrices are close to …
We revisit the possibility of relating lepton mixing angles with lepton mass hierarchies in a model-independent way. Guided by the existence of such relations in the quark sector, we first consider all the mixing angles, both in charged lepton and neutrino sectors to be related to the respective mass ratios. This allows us to calculate the leptonic mixing angles observed in neutrino oscillations as functions of the lightest neutrino mass. We show that for both normal and inverted hierarchical neutrino masses, this scenario does not give rise to correct leptonic mixing angles. We then show that…
The strategy of constraining the lepton flavor mixing from remnant CP symmetry is investigated in a rather general way. The neutrino mass matrix generally admits four remnant CP transformations which can be derived from the measured lepton mixing matrix in the charged lepton diagonal basis. Conversely, the lepton mixing matrix can be reconstructed from the postulated remnant CP transformations. All mixing angles and CP violating phases can be completely determined by the full set of remnant CP transformations or three of them. When one or two remnant CP transformations are preserved, the resul…
The current status of our knowledge of the 3-neutrino mixing parameters and of the CP violation in the lepton sector is summarised. The discrete symmetry approach to understanding the observed pattern of neutrino mixing and the related predictions for neutrino mixing angles and leptonic Dirac CP violation are reviewed.
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.
Some properties of lepton mixing and neutrino masses can be computed under the assumption of A5 and CP as a symmetry in the leptonic sector. The results show that four mixing patterns accommodate well the oscillation data, i.e. all the mixing angles are in the 3sigma confidence region. We also introduce an explicit realization of this framework in the case of the Weinberg operator where the neutrino mass spectrum can be computed.
A model-independent ansatz to describe lepton and quark mixing in a unified way is suggested based upon the Cabibbo angle. In our framework neutrinos mix in a "Bi-Large" fashion, while the charged leptons mix as the "down-type" quarks do. In addition to the standard Wolfenstein parameters (lambda, A) two other free parameters are needed to specify the physical lepton mixing matrix. Through this simple assumption one makes specific predictions for the atmospheric angle as well as leptonic CP violation in good agreement with current observations.
We consider two Ansatze for the neutrino masses and mixings in which the permutation symmetry is implemented in various orders. We discuss the possible see-saw mechanisms and the charged lepton masses for the two cases in the presence of a Higgs triplet and three Higgs doublets.
The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.
Including the generalized CP symmetry, we have performed a comprehensive scan of leptonic mixing patterns which can be obtained from finite discrete groups with order less than 2000. Both the semidirect approach and its variant are considered. The lepton mixing matrices which can admit a good agreement with experimental data can be organized into eight different categories up to possible row and column permutations. These viable mixing patterns can be completely obtained from the discrete flavor groups $Δ(6n^2)$, $D^{(1)}_{9n,3n}$, $A_5$ and $Σ(168)$ combined with CP symmetry. We perform a det…
Using discrete flavour group, $A_5$, combined with generalised CP, we study the mixing parameter correlations which arise from breaking to residual symmetries in the neutrino, $G_ν=\mathbb{Z}_2\times \text{CP}$, and charged lepton sectors, $G_{e}=\mathbb{Z}_2$. By focusing on patterns that agree with current experimental data we demonstrate that non-trivial leptonic phases are predicted and discuss a number of distinctive correlations between mixing parameters.
Flavour symmetries have been used to constrain both quark and lepton mixing parameters. In particular, they can be used to completely fix the mixing angles. For the lepton sector, assuming that neutrinos are Majorana particles, we have derived the complete list of mixing patterns achievable in this way, as well as the symmetry groups associated to each case. Partial computer scans done in the past have hinted that such list is limited, and this does indeed turn out to be the case. In addition, most mixing patterns are already 3-sigma excluded by neutrino oscillation data.
