Supersymmetric SO(10) GUTs with sliding scales

TL;DR

This paper constructs and analyzes supersymmetric SO(10) GUT models with extended gauge groups at intermediate scales, using a novel 'sliding mechanism' to achieve unification across various energy scales, and explores their experimental testability.

Contribution

It introduces the 'sliding mechanism' for unification in SO(10) models with multiple intermediate scales, allowing for flexible gauge symmetry breaking patterns and potential LHC-accessible new gauge bosons.

Findings

Over 50 variants with one intermediate scale and low LR symmetry scale.

Thousands of variants with multiple intermediate scales, including very low Pati-Salam scales.

Classification of soft SUSY-breaking invariants indicating model classes and beyond-MSSM physics scales.

Abstract

We construct lists of supersymmetric models with extended gauge groups at intermediate steps, all of which are based on 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 (PS) 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 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 an 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 PS scales. We also discuss possible experimental tests of the models from measurements of SUSY 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-MSSM physics, even in case the extended gauge group is broken at an energy beyond the reach of the LHC.