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 ${\bf 10} \oplus \overline{\bf 126}$ 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 LEP chargino limit; and (iii) $\mu\to e\gamma$, the muon $g-2$, and electric dipole moments. We perform a global scan over the soft-breaking parameters, complemented by a constrained-$\mu$ 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 $M_{H_C}$ for the proton decay normalization and to a constrained-$\mu$ treatment, what survives is a narrow mini-split region: heavy, multi-tens-of-TeV scalars with $m_0 \gtrsim 7.7$~TeV and $\tan\beta \lesssim 9$. We also examine the fate of the lightest supersymmetric particle as a dark matter candidate, in both the universal model and its free-$\mu$ 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.