Tri-bimaximal mixing and the neutrino oscillation data

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.

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Modern Tests of Lorentz Invariance

R-Parity-violating supersymmetry

This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A₄, S₄ and Δ(96).

https://iopscience.iop.org/article/10.1088/0034-4885/76/5/056201/pdf

Neutrino Mass and Mixing with Discrete Symmetry

This article reviews the current theoretical and experimental status of the field of muon decay and its potential to search for new physics beyond the standard model. The importance of rare muon processes with lepton flavor violation is highly stressed, together with precision measurements of normal muon decay. Recent up-to-date motivations of lepton flavor violation based on supersymmetric models, in particular supersymmetric grand unified theories, are described along with other theoretical models. Future prospects of experiments and muon sources of high intensity for further progress in this field are also discussed.

Muon decay and physics beyond the standard model

A search for ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}$ oscillations has been conducted with the LSND apparatus using ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ from ${\ensuremath{\pi}}^{+}$ decay in flight. Two analyses observe a total of 40 beam-on high-energy (60--200 MeV) electron events consistent with the ${\ensuremath{\nu}}_{e}\mathrm{C}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}X$ inclusive reaction. This number is significantly above the $21.9\ifmmode\pm\else\textpm\fi{}2.1$ events expected from the ${\ensuremath{\nu}}_{e}$ contamination in the beam and the beam-off background. If interpreted as an oscillation signal, the observed oscillation probability of $(2.6\ifmmode\pm\else\textpm\fi{}1.0\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ is consistent with the previously reported ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{e}$ oscillation evidence from LSND.

Results on ν μ → ν e Neutrino Oscillations from the LSND Experiment

A search for ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{e}$ oscillations has been conducted at the Los Alamos Meson Physics Facility using ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ from ${\ensuremath{\pi}}^{+}$ decay in flight. An excess in the number of beam-related events from the ${\ensuremath{\nu}}_{e}\stackrel{\ensuremath{\rightarrow}}{C}{e}^{\ensuremath{-}}X$ inclusive reaction is observed. The excess is too large to be explained by normal ${\ensuremath{\nu}}_{e}$ contamination in the beam at a confidence level greater than 99%. If interpreted as an oscillation signal, the observed oscillation probability of $(2.6\ifmmode\pm\else\textpm\fi{}1.0\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ is consistent with the previously reported ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\overline{\ensuremath{\nu}}}_{e}$ oscillation evidence from LSND.

https://arxiv.org/pdf/nucl-ex/9706006.pdf

Results on ν μ →ν e oscillations from pion decay in flight neutrinos

The MiniBooNE experiment will unambiguously confirm or refute the existence of the neutrino oscillation signal seen by the liquid scintillator neutrino detector (LSND) experiment at Los Alamos National Laboratory. MiniBooNE will search for the appearance of electron neutrinos in a beam of muon neutrinos. The MiniBooNE detector is a 12-m-diameter sphere filled with mineral oil and instrumented with photomultiplier tubes. The properties of the mineral oil chosen to fill this Cerenkov detector will be important to the experiment. The production of scintillation light in the oil, the attenuation of light across the detector, and the index of refraction of the oil are all important properties that must be known in order to properly model the detector. Fluorescence of the oil, optical dispersion, and oil density are also important quantities. The fluorescence spectra for several pure mineral oils as well as mineral oils doped with a small amount of various fluors were measured to determine the expected scintillation spectra from those oils. Index of refraction measurements were made in order to determine the Cerenkov angle and the dispersion for each oil. Attenuation tests were performed to rind an oil with maximal attenuation length and with no abnormal absorption features. This paper presents measurements of some of the oil properties, which are made at Fermilab using several experimental setups. Based on the results of these tests (and a price within budget constraints), Marcol 7 oil was selected for the MiniBooNE experiment.

G. T. Garvey

Papers

Results on ν μ → ν e Neutrino Oscillations from the LSND Experiment

Results on ν μ →ν e oscillations from pion decay in flight neutrinos

Mineral oil tests for the MiniBooNE detector