New Weak-Scale Physics from SO(10) with High-Scale Supersymmetry

Gauge coupling unification and the stability of the Higgs vacuum are among two of the cherished features of low-energy supersymmetric models. Putting aside questions of naturalness, supersymmetry might only be realised in nature at very high energy scales. If this is the case, the preservation of gauge coupling unification and the stability of the Higgs vacuum would certainly require new physics, but it need not necessarily be at weak scale energies. New physics near the unification scale could in principle ensure Grand Unification, while new physics below $\mu \sim 10^{10}$ GeV could ensure the stability of the Higgs vacuum. Surprisingly however, we find that in the context of a supersymmetric SO(10) Grand Unified Theory, gauge coupling unification and the Higgs vacuum stability, when taken in conjunction with existing phenomenological constraints, require the presence of $\mathcal{O}$(TeV)-scale physics. This weak-scale physics takes the form of a complex scalar SU(2)$_L$ triplet with zero hypercharge, originating from the $\mathbf{210}$ of SO(10).
Comment: 30 pages, 20 figures