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

The Majorana nature of neutrinos can be experimentally verified only via lepton-number violating processes involving charged leptons. We study 36 lepton-number violating (LV ) processes from the decays of tau leptons and pseudoscalar mesons. These decays are absent in the Standard Model but, in presence of Majorana neutrinos in the mass range ∼ 100 MeV to 5 GeV, the rates for these processes would be enhanced due to their resonant contribution. We calculate the transition rates and branching fractions and compare them to the current bounds from direct experimental searches forL = 2 tau and rare meson decays. The experimental non-observation of such LV processes places stringent bounds on the Majorana neutrino mass and mixing and we summarize the existing limits. We also extend the search to hadron collider experiments. We find that, at the Tevatron with 8 fb −1 integrated luminosity, there could be 2σ (5σ) sensitivity for resonant production of a Majorana neutrino in the � ± � ± modes in the mass range of ∼ 10 − 180 GeV (10 − 120 GeV). This reach can be extended to ∼ 10 − 375 GeV (10 − 250 GeV) at the LHC of 14TeV with 100 fb −1 . The production cross section at the LHC of 10TeV is also presented for comparison. We study the � ± e ± modes as well and find that the signal could be large enough even taking into account the current bound from neutrinoless double-beta decay. The signal from the gauge boson fusion channel W + W + → l + l + at the LHC is found to be very weak given the rather small mixing parameters. We comment on the search strategy when a τ lepton is involved in the final state.

https://iopscience.iop.org/article/10.1088/1126-6708/2009/05/030/pdf

The Search for Heavy Majorana Neutrinos

R-Parity-violating supersymmetry

Model of 'Calculable' Majorana Neutrino Masses

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 Neutrino 2004, as well as state-of-the-art solar and atmospheric neutrino flux calculations. We give the two-neutrino solar + KamLAND results, and the 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 α ≡ ΔmSOL2/ΔmATM2 as well as sin2 θ13, 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 evidence in view of the most recent developments.

https://iopscience.iop.org/article/10.1088/1367-2630/6/1/122/pdf

Status of global fits to neutrino oscillations

A Theory of Lepton Number Violation, Neutrino Majorana Mass, and Oscillation

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A Theory of Lepton Number Violation, Neutrino Majorana Mass, and Oscillation