Abstract: The simplest realization of the inverse seesaw mechanism in a SU(3)(C) circle times SU(3)(L) circle times U(1)(X) gauge theory offers striking flavor correlations between rare charged lepton flavor violating decays and the measured neutrino oscillations parameters. The predictions follow from the gauge structure itself without the need for any flavor symmetry. Such tight complementarity between charged lepton flavor violation and neutrino oscillations renders the scenario strictly testable.

Abstract: 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.

Abstract: We study the implications of the recent measurements of R-K and R-K* by the LHCb Collaboration. We do that by adopting a model-independent approach based on the Standard Model effective field theory (SMEFT), with the dominant new physics (NP) effects encoded in the coefficients of dimension-6 operators respecting the full Standard Model (SM) gauge symmetry. After providing simplified expressions for R-K and R-K*, we determine the implications of the recent LHCb results for these observables on the coefficients of the SMEFT operators at low and high energies. We also take into account all b -> sll data, which combined lead to effective NP scenarios with SM pulls in excess of 5 sigma. Thus, the operators discussed in this paper would be the first dimension-6 terms in the SM Lagrangian to be detected experimentally. Indirect constraints on these operators are also discussed. The results of this paper transcend the singularity of the present situation and set a standard for future analyses in b -> s transitions when the NP is assumed to lie above the electroweak scale.