Geometric Shielding of the Electroweak Scale: Solving the Hierarchy Problem in the Zhang Effective Metric

The hierarchy problem—the vast discrepancy between the electroweak scale (10² GeV) and the Planck scale (10¹⁹ GeV)—remains one of the most pressing unresolved issues in particle physics. Standard Model quantum corrections to the Higgs mass diverge quadratically, requiring extreme fine-tuning unless a new symmetry or structural mechanism intervenes.

In this paper, we demonstrate that within the rotational-order geometric unification framework, the Higgs field emerges as a geometric modulus of the internal S³ fibre. The non-trivial rotational order n̂ᵃ in the 15-dimensional geometry introduces an exponential warping factor. This geometric shielding exponentially suppresses the high-scale quantum corrections to the four-dimensional effective Higgs mass, naturally stabilizing the electroweak scale without invoking low-energy supersymmetry or introducing new fundamental scalar fields. 

Unlike conventional brane-world models, this warping is sourced entirely by the internal curvature and rotational-order field, requiring no ad-hoc brane sources. The mechanism naturally explains the 17 orders of magnitude hierarchy through the geometry of the internal manifold.