Abstract: All extensions of the standard model that generate Majorana neutrino masses at the electroweak scale introduce some heavy mediators, either fermions and/or scalars, weakly coupled to leptons. Here, by “heavy,” we mean implicitly the mass range between a few 100 GeV up to, say, roughly 2 TeV, such that these particles can be searched for at the LHC. We study decay widths of these mediators for several different tree-level neutrino mass models. The models we consider range from the simplest d = 5 seesaw up to d = 11 neutrino mass models. For each of the models, we identify the most interesting parts of the parameter space, where the heavy mediator fields are particularly long lived and can decay with experimentally measurable decay lengths. One has to distinguish two different scenarios, depending on whether fermions or scalars are the lighter of the heavy particles. For fermions, we find that the decay lengths correlate with the inverse of the overall neutrino mass scale. Thus, since no lower limit on the lightest neutrino mass exists, nearly arbitrarily long decay lengths can be obtained for the case in which fermions are the lighter of the heavy particles. For charged scalars, on the other hand, there exists a maximum value for the decay length in these models. This maximum value depends on the model and on the electric charge of the scalar under consideration but can at most be of the order of a few millimeters. Interestingly, independent of the model, this maximum occurs always in a region of parameter space, where leptonic and gauge boson final states have similar branching ratios, i.e., where the observation of lepton number-violating final states from scalar decays is possible.

Abstract: We construct lists of supersymmetric models with extended gauge groups at intermediate steps, all of which are inspired by SO(10) unification. We consider three different kinds of setups: (i) the model has exactly one additional intermediate scale with a left-right (LR) symmetric group; (ii) SO(10) is broken to the LR group via an intermediate Pati-Salam scale; and (iii) the LR group is broken into SU(3)(c) X SU(2)(L) X U(1)(R) X U(1)(B-L), before breaking to the standard model (SM) group. We use sets of conditions, which we call the “sliding mechanism,” which yield unification with the extended gauge group(s) allowed at arbitrary intermediate energy scales. All models thus can have new gauge bosons within the reach of the LHC, in principle. We apply additional conditions, such as perturbative unification, renormalizability and anomaly cancellation and find that, despite these requirements, for the ansatz (i) with only one additional scale still around 50 different variants exist that can have a LR symmetry below 10 TeV. For the more complicated schemes (ii) and (iii) literally thousands of possible variants exist, and for scheme (ii) we have also found variants with very low Pati-Salam scales. We also discuss possible experimental tests of the models from measurements of supersymmetry masses. Assuming mSugra boundary conditions we calculate certain combinations of soft terms, called “invariants,” for the different classes of models. Values for all the invariants can be classified into a small number of sets, which contain information about the class of models and, in principle, the scale of beyond-minimal supersymmetric extension of the Standard Model physics, even in case the extended gauge group is broken at an energy beyond the reach of the LHC.