L. Lavoura

Is S4 the horizontal symmetry of tri-bimaximal lepton mixing?

We determine the symmetry groups under which the charged-lepton and the Majorana-neutrino mass terms are invariant. We note that those two groups always exist trivially, i.e. independently of the presence of any symmetries in the Lagrangian, and that they always have the same form. Using this insight, we re-evaluate the recent claim that, whenever lepton mixing is tri-bimaximal, S4 is the minimal unique horizontal-symmetry group of the Lagrangian of the lepton sector, with S4 being determined by the symmetries of the lepton mass matrices. We discuss two models for tri-bimaximal mixing which serve as counterexamples to this claim. With these two models and some group-theoretical arguments we illustrate that there is no compelling reason for the uniqueness of S4.

Maximal CP Violation in Lepton Mixing from a Model with Delta(27) flavour Symmetry

A bstractWe propose a simple mechanism which enforces

μ–τ interchange symmetry and lepton mixing

\left| {{U_{\mu j}}} \right| = \left| {{U_{\tau j}}} \right|\forall j = 1,2,3

Tri-bimaximal lepton mixing from symmetry only

in the lepton mixing matrix U. This implies maximal atmospheric neutrino mixing and a maximal CP-violating phase but does not constrain the reactor mixing angle θ13. We implement the proposed mechanism in two renormalizable seesaw models which have features strongly resembling those of models based on a flavour symmetry group Δ(27). Among the predictions of the models, there is a determination, although ambiguous, of the absolute neutrino mass scale, and a stringent correlation between the absolute neutrino mass scale and the effective Majorana mass in neutrinoless double-beta decay.

Flavour models for TM1 lepton mixing

We focus on the use of a μ–τ interchange symmetry to explain features of lepton mixing, especially maximal atmospheric neutrino mixing. We review two models which achieve this goal and are based on the seesaw mechanism and on the soft breaking of the family-lepton-number symmetries. We also note that that symmetry may be embedded in a generalized CP symmetry. We show that, in the context of some of our models, arguments of naturalness may be used for explaining the smallness of the mass ratio mμ / mτ.

Accidental stability of dark matter

We construct a model for tri-bimaximal lepton mixing which employs only family symmetries and their soft breaking; neither vacuum alignment nor supersymmetry, extra dimensions, or non-renormalizable terms are used in our model. It is an extension of the Standard Model making use of the seesaw mechanism with five right-handed neutrino singlets. The scalar sector comprises four Higgs doublets and one complex gauge singlet. The horizontal symmetry of our model is based on the permutation group S3 of the lepton families together with the three family lepton numbers—united this constitutes a symmetry group Δ(6∞2). The model makes no predictions for the neutrino masses.

On a possible relationship between lepton mixing and the stability of dark matter

We present a framework for lepton flavour models such that the first column of the lepton mixing matrix is . We show that the flavour symmetry group adequate for this purpose is S4. Our models are based on a vacuum alignment that can be obtained in a supersymmetric framework.

Five models for lepton mixing

A bstractWe propose that dark matter is stable as a consequence of an accidental

TEXTURE-ZERO MODEL FOR THE LEPTON MASS MATRICES

{{\mathbb{Z}}_2}

Numerical analysis of

that results from a flavour symmetry group which is the double-cover group of the symmetry group of one of the regular geometric solids. Although model-dependent, the phenomenology resembles that of a generic “inert Higgs” dark matter scheme.