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 modelbuilding 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.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. New J. Phys. 16 (2014) 045018 S F King et al 2 5 In the SM the quantum numbers are the hypercharge Y, the weak isospin T 3 , and the colour charge. 6 Where = v 174 H GeV is the vacuum expectation value (VEV) of the Higgs doublet. New J. Phys. 16 (2014) 045018 S F King et al 3 7 To be more specific, it is also possible to have intermediate cases like pseudo-Dirac [2], quasi-Dirac [3], schizophrenic [4], and so on, but in this review we will consider only the Dirac and Majorana cases. 8 This assumption is quite reasonable having in mind ( )SO 10 grand unified frameworks, where all SM fermions and the right-handed neutrino belong to a 16 multiplet. 9 The terminology I, II, and III has been introduced in [17].

The discrete flavor symmetry A 4 explains very well neutrino data at low energy, but it seems difficult to extend it to grand unified models since, in general, left-handed and right-handed fields belong to different A 4 representations. Recently a model has been proposed where all the fermions equally transform under A 4 . We study here a concrete SO10 realization of such a model providing small neutrino masses through the see-saw mechanism. We fit the charged fermion masses run up to the unification scale. Some fermion masses properties come from the SO10 symmetry while lepton mixing angles are a consequence of the A 4 properties. Moreover, our model predicts the absolute value of the neutrino masses; these are in the range m ' 0:005-0:052 eV.

We propose a new motivation for the stability of dark matter (DM). We suggest that the same nonabelian discrete flavor symmetry which accounts for the observed pattern of neutrino oscillations, spontaneously breaks to a Z2 subgroup which renders DM stable. The simplest scheme leads to a scalar doublet DM potentially detectable in nuclear recoil experiments, inverse neutrino mass hierarchy, hence a neutrinoless double beta decay rate accessible to upcoming searches, while θ13 = 0 gives no CP violation in neutrino oscillations. Introduction The existence of dark matter (DM) plays a central role in the modeling of structure formation and galaxy evolution, affecting also the cosmic microwave background. Despite the strong evidence in favor of DM, its detailed nature remains rather elusive. Viable particle physics candidates for dark matter must be electrically neutral, and provide the correct relic abundance. Therefore they must be stable over cosmological time scales. A simple way to justify the stability of the DM is by assuming some parity symmetry Z 2 , which might arise from the spontaneous breaking of an abelian U(1) gauge symmetry [1-3] 1 , or from a non-abelian discrete symmetry, as might be the case in some string models [4].Non abelian discrete symmetries are motivated by neutrino oscillation data [5,6]. Here we propose that the same symmetry explaining neutrino mixing angles is also responsible for the dark matter stability. In our simplest type-I seesaw [7] realization the flavor symmetry A 4 spontaneously breaks to Z 2 providing a stable DM candidate. We extend the scalar sector of the standard model by adding three Higgs doublets transforming as a triplet of A 4 we show that there is a consistent pattern of vacuum expectation values (vevs) for which only one of the three extra Higgs doublets takes a vev, while the other two give rise to the dark matter candidate. The model accounts for the observed pattern of mixing angles [8] indicated by current neutrino oscillation data, predicting θ 13 = 0 and inverted spectrum of neutrino masses. It will therefore be tested in upcoming double beta and neutrino oscillation searches [9], while the dark matter has potentially detectable rates within reach of nuclear recoil experiments.

Abstract:The minimal seesaw extension of the Standard SU(3) c ⊗ SU(2) L ⊗ U(1) Y Model requires two electroweak singlet fermions in order to accommodate the neutrino oscillation parameters at tree level. Here we consider a next to minimal extension where light neutrino masses are generated radiatively by two electroweak fermions: one singlet and one triplet under SU(2) L . These should be odd under a parity symmetry and their mixing gives rise to a stable weakly interactive massive particle (WIMP) dark matter candidate. For mass in the GeV-TeV range, it reproduces the correct relic density, and provides an observable signal in nuclear recoil direct detection experiments. The fermion triplet component of the dark matter has gauge interactions, making it also detectable at present and near future collider experiments.ArXiv ePrint: 1307.8134 IFIC/13-53 arXiv:1307.8134v2 [hep-ph]