Abstract: In the framework of the low -energy effective theory containing, in addition to the Standard -Model fields, heavy neutral leptons (HNLs), we compute the decay rates of neutral and charged kaons into HNLs. We consider both lepton -number -conserving and lepton -number -violating four-fermion operators, taking into account also the contribution of active -heavy neutrino mixing. Assuming that the produced HNLs are longlived, we perform simulations and calculate the sensitivities of future long -lived -particle (LLP) detectors at the high -luminosity LHC as well as the near detector of the Deep Underground Neutrino Experiment (DUNE -ND) to the considered scenario. When applicable, we also recast the existing bounds on the minimal mixing case obtained by NA62, T2K, and PS191. Our findings show that, while the future LHC LLP detectors can probe currently allowed parameter space only in certain benchmark scenarios, DUNE -ND should be sensitive to parameter space beyond the current bounds in almost all the benchmark scenarios, and, for some of the effective operators considered, it can even probe new -physics scales in excess of 3000 TeV.

Abstract: Lepton number violation is searched for at the LHC using same-sign leptons plus jets. The standard lore is that the ratio of same-sign lepton to opposite-sign lepton events, R-ll, is equal to R-ll = 1 (R-ll = 0) for Majorana (Dirac) neutrinos. We clarify under which conditions the ratio Rll can assume values different from 0 and 1, and we argue that the precise value 0 < R-ll < 1 is controlled by the mass splitting versus the width of the quasi-Dirac resonances. A measurement of R-ll not equal 0, 1 would then contain valuable information about the origin of neutrino masses. We consider as an example the inverse seesaw mechanism in a left-right symmetric scenario, which is phenomenologically particularly interesting since all the heavy states in the high energy completion of the model could be within experimental reach. A prediction of this scenario is a correlation between the values of R-ll and the ratio between the rates for heavy neutrino decays into standard model gauge bosons, and into three body final states ljj mediated by off-shell W-R exchange.

Abstract: We study a supersymmetric version of the seesaw mechanism type III. The model consists of the minimal supersymmetric extension of the standard model particle content plus three copies of 24 superfields. The fermionic part of the SU(2) triplet contained in the 24 is responsible for the type-III seesaw, which is used to explain the observed neutrino masses and mixings. Complete copies of 24 are introduced to maintain gauge coupling unification. These additional states change the beta functions of the gauge couplings above the seesaw scale. Using minimal Supergravity boundary conditions, we calculate the resulting supersymmetric mass spectra at the electroweak scale using full 2-loop renormalization group equations. We show that the resulting spectrum can be quite different compared to the usual minimal Supergravity spectrum. We discuss how this might be used to obtain information on the seesaw scale from mass measurements. Constraints on the model space due to limits on lepton flavour violating decays are discussed. The main constraints come from the bounds on μ-> e gamma but there are also regions where the decay tau -> μgamma gives stronger constraints. We also calculate the regions allowed by the dark matter constraint. For the sake of completeness, we compare our results with those for the supersymmetric seesaw type II and, to some extent, with type I.