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 $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_R\times U(1{)}_{B-L}$, 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.

• Received 31 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.075010