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.

Abstract: We discuss lepton number violation in three units. From an effective field theory point of view, Delta L = 3 processes can only arise from dimension 9 or higher operators. These operators also violate baryon number, hence many of them will induce proton decay. Given the high dimensionality of these operators, in order to have a proton half-life in the observable range, the new physics associated to Delta L = 3 processes should be at a scale as low as 1 TeV. This opens up the possibility of searching for such processes not only in proton decay experiments but also at the LHC. In this work we analyze the relevant d = 9, 11, 13 operators which violate lepton number in three units. We then construct one simple concrete model with interesting low- and high-energy phenomenology.

Abstract: Models based on the extended SU(3)(C) x SU(3)(L) x U(1)(X) (331) gauge group usually follow a common pattern: two families of left-handed quarks are placed in anti triplet representations of the SU(3)(L) group; the remaining quark family, as well as the left-handed leptons, are assigned to triplets (or vice-versa). In this work we present a flipped 331 model where this scheme is reversed: all three quark families are in the same representation and it is the lepton families which are discriminated by the gauge symmetry. We discuss fermion masses and mixing, as well as Z' interactions, in a minimal model implementing this idea.