Grand Unified Origin of Enhanced Scalar Couplings: Connecting Radiative Electroweak Symmetry Breaking to SO(10) Dynamics

Abstract

We propose that the enhanced Higgs quartic coupling required by radiatively broken electroweak symmetry (RBEWS) emerges naturally from SO(10) grand unification. Our previous analysis demonstrated that a coupling enhancement factor $k = \lambda_{\rm enhanced}/\lambda_{\rm SM}$ leads to absolute vacuum stability with a UV Landau pole near the GUT scale for $k \gtrsim 1.03$. The RBEWS prediction $e_{125} = 7.2$ of Steele and Wang, when properly translated from the Coleman-Weinberg scheme at the electroweak VEV to the $\overline{\rm MS}$ scheme at $M_t$ via scheme conversion and scale-dependent ratio evolution, yields $k(M_t) \approx 6.0$--$6.4$, corresponding to a UV pole at $\Lambda_{\rm UV} \sim {1.5\text{--}2} \times 10^{16}$~GeV -- remarkably close to the GUT scale $M_{\rm GUT} \sim 2 \times 10^{16}$~GeV. We argue this coincidence is not accidental: the UV pole signals the scale where the Standard Model effective description must be embedded into the full SO(10) structure. We derive threshold corrections from SO(10) scalar sectors containing $\mathbf{10}_H$, $\mathbf{\overline{126}}_H$, and $\mathbf{45}_H$ representations, showing that portal couplings between the light Higgs doublet and heavy GUT scalars can generate enhancement factors of order $k \sim 5$--$10$ at the matching scale. The Coleman-Weinberg mechanism operating within a classically scale-invariant GUT scalar potential provides a dynamical origin for both RBEWS and the hierarchy between $M_{\rm GUT}$ and the electroweak scale.