Self-interacting dark matter has been proposed as a solution to the small-scale structure problems, such as the observed flat cores in dwarf and low surface brightness galaxies. If scattering takes place through light mediators, the scattering cross section relevant to solve these problems may fall into the non-perturbative regime leading to a non-trivial velocity dependence, which allows compatibility with limits stemming from cluster-size objects. However, these models are strongly constrained by different observations, in particular from the requirements that the decay of the light mediator is sufficiently rapid (before Big Bang Nucleosynthesis) and from direct detection. A natural solution to reconcile both requirements are inelastic endothermic interactions, such that scatterings in direct detection experiments are suppressed or even kinematically forbidden if the mass splitting between the two-states is sufficiently large. Using an exact solution when numerically solving the Schrödinger equation, we study such scenarios and find regions in the parameter space of dark matter and mediator masses, and the mass splitting of the states, where the small scale structure problems can be solved, the dark matter has the correct relic abundance and direct detection limits can be evaded.

The goal of the works on which this talk is based is to relate a direct detection signal with neutrino limits from the Sun independently of the astrophysics. In order to achieve this we derive a halo-independent lower bound on the dark matter capture rate in the Sun from a direct detection signal, with which one can set upper limits on the branching ratios into different channels from the absence of a high-energy neutrino flux in neutrino observatories. We also extend this bound to the case of inelastic scattering, both endothermic and exothermic. From two inelastic signals we show how the dark matter mass, the mass difference of the states and the couplings to neutrons and protons can be obtained. Furthermore, one can also pin down the exothermic/endothermic nature of the scattering, and therefore a precise lower bound on the solar capture rate is predicted. We also discuss isospin violation and uncertainties due to form factors.

We study the general Zee model, which includes an extra Higgs scalar doublet and a new singly-charged scalar singlet. Neutrino masses are generated at one-loop level, and in order to describe leptonic mixing, both the Standard Model and the extra Higgs scalar doublets need to couple to leptons (in a type-III two-Higgs doublet model), which necessarily generates large lepton flavor violating signals, also in Higgs decays. Imposing all relevant phenomenological constraints and performing a full numerical scan of the parameter space, we find that both normal and inverted neutrino mass orderings can be fitted, although the latter is disfavored with respect to the former. In fact, inverted ordering can only be accommodated if theta(23) turns out to be in the first octant. A branching ratio for h -> tau mu of up to 10(-2) is allowed, but it could be as low as 10(-6). In addition, if future expected sensitivities of tau -> mu gamma are achieved, normal ordering can be almost completely tested. Also, mu e conversion is expected to probe large parts of the parameter space, excluding completely inverted ordering if no signal is observed. Furthermore, non-standard neutrino interactions are found to be smaller than 10(-6), which is well below future experimental sensitivity. Finally, the results of our scan indicate that the masses of the additional scalars have to be below 2.5 TeV, and typically they are lower than that and therefore within the reach of the LHC and future colliders.

We study lepton violating Higgs (HLFV) decays, first from the effective field theory (EFT) point of view, and then analysing the different high-energy realizations of the operators of the EFT, highlighting the most promising models. We argue why two Higgs doublet models can have a BR(h -> tau mu) similar to 0:01, and why this rate is suppressed in all other realizations including vector-like leptons. We further discuss HLFV in the context of neutrino mass models: in most cases it is generated at one loop giving always BR (h -> tau mu) < 10(-4) and typically much less, which is beyond experimental reach. However, both the Zee model and extended left-right symmetric models contain extra SU(2) doublets coupled to leptons and could in principle account for the observed excess, with interesting connections between HLFV and neutrino parameters.