A plausible explanation for the lightness of neutrino masses is that neutrinos are massless at tree level, with their mass (typically Majorana) being generated radiatively at one or more loops. The new couplings, together with the suppression coming from the loop factors, imply that the new degrees of freedom cannot be too heavy (they are typically at the TeV scale). Therefore, in these models there are no large mass hierarchies and they can be tested using different searches, making their detailed phenomenological study very appealing. In particular, the new particles can be searched for at colliders and generically induce signals in lepton-flavor and lepton-number violating processes (in the case of Majorana neutrinos), which are not independent from reproducing correctly the neutrino masses and mixings. The main focus of the review is on Majorana neutrinos. We order the allowed theory space from three different perspectives: (i) using an effective operator approach to lepton number violation, (ii) by the number of loops at which the Weinberg operator is generated, (iii) within a given loop order, by the possible irreducible topologies. We also discuss in more detail some popular radiative models which involve qualitatively different features, revisiting their most important phenomenological implications. Finally, we list some promising avenues to pursue.

We investigate lepton flavor violation in the scotogenic model proposed by Ma in which neutrinos acquire non-zero masses at the 1-loop level. Although some works exist in this direction, they have mainly focused on the radiative decay ℓ α → ℓ β γ. Motivated by the promising new projects involving other low-energy processes, we derive complete analytical expressions for ℓ α → 3 ℓ β and µ − e conversion in nuclei, and numerically study their impact on the phenomenology. We will show that these processes can actually have rates larger than the one for ℓ α → ℓ β γ, thus providing more stringent constraints and better experimental perspectives.

The µνSSM has been proposed to solve simultaneously the µ-problem of the MSSM and explain current neutrino data. The model breaks lepton number as well as R-parity. In this paper we study the phenomenology of this proposal concentrating on neutrino masses and the decay of the lightest supersymmetric particle (LSP). At first we investigate in detail the µνSSM with one generation of singlets, which can explain all neutrino data, once 1-loop corrections are taken into account. Then we study variations of the model with more singlets, which can generate all neutrino masses and mixings at tree-level. We calculate the decay properties of the lightest supersymmetric particle, assumed to be the lightest neutralino, taking into account all possible final states. The parameter regions where the LSP decays within the LHC detectors but with a length large enough to show a displaced vertex are identified. Decay branching ratios of certain final states show characteristic correlations with the measured neutrino angles, allowing to test the model at the LHC. Finally we briefly discuss possible signatures, which allow to distinguish between different R-parity breaking models.

The LHCb collaboration has recently reported on some anomalies in b → s transitions. In addition to discrepancies with the Standard Model (SM) predictions in some angular observables and branching ratios, an intriguing hint for lepton universality violation was found. Here we propose a simple model that extends the SM with a dark sector charged under an additional U(1) gauge symmetry. The spontaneous breaking of this symmetry gives rise to a massive Z boson, which communicates the SM particles with a valid dark matter candidate, while solving the b → s anomalies with contributions to the relevant observables.