Abstract
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.
Highlights
In the Standard Model (SM) we have three families of fermions
The indirect approach is used in association with sequential dominance, in which the lepton mixing arises from the neutrino sector as a result of the type I seesaw mechanism, with one of the right-handed neutrinos being mainly responsible for the atmospheric neutrino mass and a second right-handed neutrino being mainly responsible for the solar neutrino mass while a third right-handed neutrino is approximately decoupled from the seesaw mechanism, leading to a normal neutrino mass hierarchy
With the measurement of the reactor angle we have entered the era of experimental precision in the lepton mixing, rather like in the quark sector but still far behind it
Summary
In the Standard Model (SM) we have three families of fermions. In each family we have two kinds of quarks, the up-quark with electric charge Q = 2/3 and the down-quark with Q = −1/3, as well as two kinds of leptons, the charged leptons with Q = −1 and the neutrino with Q = 0. Another possibility is to directly fit the lepton mixing observable without introducing any particular ansatz but using some non-Abelian discrete flavour symmetry to predict the mixing angles, like for instance in [67]. If experiments give us an indication for a non-maximal atmospheric angle, the three mixing angles could be considered in first approximation about of similar order and may be difficult to see any underlying mixing pattern In this case the neutrino mass matrix can be anarchical [73].
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