We review the present status of global analyses of neutrino oscillations, taking into account the most recent neutrino data including the latest KamLAND and K2K updates presented at Neutrino2004, as well as state-of-the-art solar and atmospheric neutrino flux calculations. We give the two-neutrino solar + KamLAND results, as well as two-neutrino atmospheric + K2K oscillation regions, discussing in each case the robustness of the oscillation interpretation against departures from the Standard Solar Model and the possible existence of non-standard neutrino physics. Furthermore, we give the best fit values and allowed ranges of the three-flavour oscillation parameters from the current worlds' global neutrino data sample and discuss in detail the status of the small parameters $\alpha \equiv \Dms/\Dma$ as well as $\sin^2\theta_{13}$, which characterize the strength of CP violating effects in neutrino oscillations. We also update the degree of rejection of four-neutrino interpretations of the LSND anomaly in view of the most recent developments.

Status of global fits to neutrino oscillations

The origin of fermion mass hierarchies and mixings is one of the unresolved and most difficult problems in high-energy physics. One possibility to address the flavour problems is by extending the standard model to include a family symmetry. In the recent years it has become very popular to use non-Abelian discrete flavour symmetries because of their power in the prediction of the large leptonic mixing angles relevant for neutrino oscillation experiments. Here we give an introduction to the flavour problem and to discrete groups that have been used to attempt a solution for it. We review the current status of models in light of the recent measurement of the reactor angle, and we consider different model-building directions taken. The use of the flavons or multi-Higgs scalars in model building is discussed as well as the direct versus indirect approaches. We also focus on the possibility of experimentally distinguishing flavour symmetry models by means of mixing sum rules and mass sum rules. In fact, we illustrate in this review the complete path from mathematics, via model building, to experiments, so that any reader interested in starting work in the field could use this text as a starting point in order to obtain a broad overview of the different subject areas.

https://iopscience.iop.org/article/10.1088/1367-2630/16/4/045018/pdf

Neutrino mass and mixing: from theory to experiment

There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups. Applying this connection to the tribimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely S{sub 4}, the permutation group of four objects.

Unique horizontal symmetry of leptons

In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of (λC) (with λC being the Cabibbo angle), arising from the diagonalization of the charged lepton masses, such that δsin2θ12 ~ sinθ13 ~ (λC) while δsin2θ23 ~ (λC2), we construct a model based on the discrete group S4 where those properties are naturally realized. The model is supersymmetric in 4-dimensions and the complete flavour group is S4 × Z4 × U(1)FN, which also allows to reproduce the hierarchy of the charged lepton spectrum. The only fine tuning needed in the model is to reproduce the small observed value of r = Δm2sun/Δm2atm. Once the relevant parameters are set to accommodate r then the spectrum of light neutrinos shows a moderate normal hierarchy and is compatible, within large ambiguities, with the constraints from leptogenesis as an explanation of the baryon asymmetry in the Universe.

/pdf/revisiting-bimaximal-neutrino-mixing-in-a-model-with-s-4-23q4dpbd6p.pdf

Revisiting Bimaximal Neutrino Mixing in a Model with S(4) Discrete Symmetry

https://digital.csic.es/bitstream/10261/15673/1/bazzocchi.pdf

Fermion Masses and Mixings in a S(4)-based Model

We study a supersymmetric extension of the Standard Model based on discrete A4xZ3xZ4 flavor symmetry. We obtain quark mixing angles as well as a realistic fermion mass spectrum and we predict tribimaximal leptonic mixing by a spontaneous breaking of A4. The top quark Yukawa interaction is present at the renormalizable level in the superpotential while all the other Yukawa interactions arise only at higher orders. We study the Higgs potential and show that it can potentially solve the so called vacuum alignment problem. The leading order predictions are not spoiled by subleading corrections.

A SUSY A4 model for fermion masses and mixings

We study a supersymmetric extension of the Standard Model based on discrete A4 × Z3 × Z4 flavor symmetry. We obtain quark mixing angles as well as a realistic fermion mass spectrum and we predict tribimaximal leptonic mixing by a spontaneous breaking of A4. The top quark Yukawa interaction is present at the renormalizable level in the superpotential while all the other Yukawa interactions arise only at higher orders. We study the Higgs potential and show that it can potentially solve the so called vacuum alignment problem. The leading order predictions are not spoiled by subleading corrections.

S. Kaneko

Papers

A SUSY A4 model for fermion masses and mixings

A SUSY A(4) model for fermion masses and mixings