Abstract
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).
Highlights
One of the most conspicuous null results of the LHC run I and run II so far has been the lack of discovery of supersymmetry (SUSY) [1] near the electroweak scale
While there have been many studies of supersymmetry at the multi-TeV scale, we instead examine the second alternative, namely that of high-scale supersymmetry [2,3]. This is partly motivated by the possibility that an EeV mass gravitino may provide the correct relic density of dark matter [4] if the supersymmetry-breaking scale lies above the inflationary scale, mI ≃ 3 × 1013 GeV
Since yt runs to large values in the IR, while g2 does not run substantially, we find that as long as R ≲ jαj, m2HðmtÞ < 0, and radiative electroweak symmetry breaking (EWSB) is achieved
Summary
One of the most conspicuous null results of the LHC run I and run II so far has been the lack of discovery of supersymmetry (SUSY) [1] near the electroweak scale. We show how the SO(10) GUT provides a viable embedding of high-scale supersymmetry, with a stable Higgs vacuum and correct gauge coupling unification, but only as long as there is a TeVscale particle in the spectrum. The unmixed fermion masses (listed in Table I) remain the same as in [15,39], since these are the Higgsinos associated with the GUT scalar Higgs bosons, and do not receive corrections from SUSY breaking. Exception of the G state, we use the mixed states (and their masses) only in the threshold corrections necessary for obtaining gauge coupling unification, and they will not be considered as candidates for a possible light scalar. All other MSSM particles, and the fermion partners of the lightest GUT scalar state must be included in the running above this scale
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