Updated analysis of minimal supersymmetric SO(10) with a universal soft spectrum

Abstract

We update the analysis of minimal supersymmetric $\SO{10}$ grand unification with a universal, constrained-MSSM-like soft-breaking spectrum. A pair of Yukawa matrices in the $\rep{10}\oplus\overline{\rep{126}}$ Higgs sector fixes the charged fermion masses and quark mixing, the baryon number-violating dimension-five operators that mediate proton decay, and the right-handed neutrino Majorana masses of the type-I seesaw. The simultaneously imposed constraints include: (i) gauge coupling unification and vacuum stability; (ii) dimension-five proton decay (the dimension-six gauge mode also computed and negligible), the $125$-GeV Higgs mass, and the Large Electron-Positron Collider (LEP) chargino limit; and (iii) $μ\to eγ$, the muon $g-2$, and electric dipole moments. We perform a global scan over the soft-breaking parameters, complemented by a constrained-$μ$ cross-check that fixes the electroweakino sector from the GUT-scale boundary conditions through radiative electroweak symmetry breaking. Subject to a single effective colored Higgs scale $\MHC$ for the proton decay normalization (common to unification and decay, though in a general color triplet mass matrix the two can differ) and to a constrained-$μ$ treatment, what survives is a narrow mini-split region: heavy, multi-tens-of-TeV scalars with $\mzero \gtrsim 11.0$~TeV for a dressing electroweakino mass $m_χ=1$~TeV and $\tb \lesssim 8.0^{+5.5}_{-2.0}$, the uncertainty being the Higgs mass theory error. We also examine the fate of the lightest supersymmetric particle as a dark matter candidate, in both the universal model and its free-$μ$ non-universal-Higgs-mass extension. The surviving region is sharply bounded and testable in the coming decade, most directly by Hyper-Kamiokande proton decay and electroweakino searches, with dark matter direct detection and electric dipole moment experiments.