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].

Abstract. We present a comprehensive review of keV-scale sterile neutrino Dark Matter, collecting views and insights from all disciplines involved -cosmology, astrophysics, nuclear, and particle physics -in each case viewed from both theoretical and experimental/observational perspectives. After reviewing the role of active neutrinos in particle physics, astrophysics, and cosmology, we focus on sterile neutrinos in the context of the Dark Matter puzzle. Here, we first review the physics motivation for sterile neutrino Dark Matter, based on challenges and tensions in purely cold Dark Matter scenarios. We then round out the discussion by critically summarizing all known constraints on sterile neutrino Dark Matter arising from astrophysical observations, laboratory experiments, and theoretical considerations. In this context, we provide a balanced discourse on the possibly positive signal from X-ray observations. Another focus of the paper concerns the construction of particle physics models, aiming to explain how sterile neutrinos of keV-scale masses could arise in concrete settings beyond the Standard Model of elementary particle physics. The paper ends with an extensive review of current and future astrophysical and laboratory searches, highlighting new ideas and their experimental challenges, as well as future perspectives for the discovery of sterile neutrinos.

Structure formation at small cosmological scales provides an important frontier for dark matter (DM) research. Scenarios with small DM particle masses, large momenta or hidden interactions tend to suppress the gravitational clustering at small scales. The details of this suppression depend on the DM particle nature, allowing for a direct link between DM models and astrophysical observations. However, most of the astrophysical constraints obtained so far refer to a very specific shape of the power suppression, corresponding to thermal warm dark matter (WDM), i.e., candidates with a Fermi-Dirac or Bose-Einstein momentum distribution. In this work we introduce a new analytical fitting formula for the power spectrum, which is simple yet flexible enough to reproduce the clustering signal of large classes of non-thermal DM models, which are not at all adequately described by the oversimplified notion of WDM. We show that the formula is able to fully cover the parameter space of sterile neutrinos (whether resonantly produced or from particle decay), mixed cold and warm models, fuzzy dark matter, as well as other models suggested by effective theory of structure formation (ETHOS). Based on this fitting formula, we perform a large suite of N -body simulations and we extract important nonlinear statistics, such as the matter power spectrum and the halo mass function. Finally, we present first preliminary astrophysical constraints, based on linear theory, from both the number of Milky Way satellites and the Lyman-α forest. This paper is a first step towards a general and comprehensive modeling of small-scale departures from the standard cold DM model.

We perform a detailed and illustrative study of the production of keV sterile neutrino Dark Matter (DM) by decays of singlet scalars in the early Universe. In the current study we focus on providing a clear and general overview of this production mechanism. For the first time we study all regimes possible on the level of momentum distribution functions, which we obtain by solving a system of Boltzmann equations. These quantities contain the full information about the production process, which allows us to not only track the evolution of the DM generation but to also take into account all bounds related to the spectrum, such as constraints from structure formation or from avoiding too much dark radiation. In particular we show that this simple production mechanism can, depending on the regime, lead to strongly non-thermal DM spectra which may even feature more than one peak in the momentum distribution. These cases could have particularly interesting consequences for cosmological structure formation, as their analysis requires more refined tools than the simplistic estimate using the free-streaming horizon. Here we present the mechanism including all concepts and subtleties involved, for now using the assumption that the effective number of relativistic degrees of freedom is constant during DM production, which is applicable in a significant fraction of the parameter space. This allows us to derive analytical results to back up our detailed numerical computations, thus leading to the most comprehensive picture of keV sterile neutrino DM production by singlet scalar decays that exists up to now. *

We propose a new production mechanism for keV sterile neutrino Dark Matter. In our setting, we assume the existence of a scalar singlet particle which never entered thermal equilibrium in the early Universe, since it only couples to the Standard Model fields by a really small Higgs portal interaction. For suitable values of this coupling, the scalar can undergo the so-called freeze-in process, and in this way be efficiently produced in the early Universe. These scalars can then decay into keV sterile neutrinos and produce the correct Dark Matter abundance. While similar settings in which the scalar does enter thermal equilibrium and then freezes out have been studied previously, the mechanism proposed here is new and represents a versatile extension of the known case. We perform a detailed numerical calculation of the DM production using a set of coupled Boltzmann equations, and we illustrate the successful regions in the parameter space. Our production mechanism notably can even work in models where active-sterile mixing is completely absent. * no primordial lepton asymmetry is present in the early Universe [17,18]. Indeed, a large enough primordial lepton asymmetry could lead to a resonant transition -the so-called Shi-Fuller mechanism [46]-producing a considerable amount of sterile neutrinos with a cooler non-thermal spectrum, in addition to the ones produced by the DW mechanism. In this way, some bounds could be evaded. On the other hand, in frameworks where the SM gauge group is extended, the sterile neutrinos could be charged non-trivially under the full gauge group and be sterile only with respect to SM interactions. In this case, although this is not compulsory [47], thermal production of keV neutrinos could be revived [48,49]. However, this mechanism would generically produce too much DM and by this overclose the Universe, thus requiring some dilution by the production of additional entropy [50]. Moreover, it could get into trouble with bounds from Big Bang nucleosynthesis [51].Probably the most versatile production mechanism from a particle physics point of view is the non-thermal production of keV sterile neutrinos by the decays of particles [52,53,54,55,56], in particular of singlet scalars. Examples of this production mechanism exists for the scalar being an inflaton [57,58] or a more general equilibrated scalar singlet particle [59,60]. This case is particularly interesting because it tends to lead to smaller bounds on the mass of the keV neutrino, a desirable feature, since keV-neutrinos with too large masses could be in danger with X-ray bound. For a recent collections of observational bounds from the non-observation of the decay into a light neutrino and a photon, N 1 → νγ, see Refs. [17,18,61] and references therein. 1 The aim of this paper is to study a variant of the scalar decay production mechanism discussed in Refs. [59,60]. The decisive point is that the scalar σ, which decays into the keV neutrinos, σ → N 1 N 1 , has to be efficiently produced in the early Universe, as otherwise it would ...