P-101:The Geometric Dissolution of the Gauge Hierarchy Problem — From Geometric Dilution to Non-perturbative Enhancement(v1.1)

Abstract:

The gauge hierarchy problem — the enormous seventeen-orders-of-magnitude gap between the electroweak scale v_H ≈ 246 GeV and the Planck scale M_Pl ≈ 1.22×10¹⁹ GeV — is regarded as the deepest "naturalness crisis" of the Standard Model. Within the mainstream paradigm, maintaining this hierarchy requires extreme fine-tuning, which has driven decades of exploration of beyond-Standard-Model new physics such as supersymmetry, extra dimensions, and composite Higgs. Starting from Space Ontology, this paper demonstrates that the gauge hierarchy is not a problem to be "solved" by new physics, but rather an inevitable consequence of spatial geometry. We rigorously derive: the vacuum expectation value is determined by v_H² = κ M_Pl² / G(κ), where G(κ) ≈ 4.2×10³¹ is the geometric dilution factor, describing the "thinning out" of the chiral structure of space from the Planck scale to the electroweak scale; the Higgs mass is given by m_H = √(2κ³/G(κ)) · e^(c/(2κ)) · M_Pl, where the e^(c/κ) factor (c ≈ 0.10) originates from the non-perturbative enhancement of the bounce instanton. The essence of the hierarchy problem is thereby reduced to the product of three geometric factors, all determined by the single free parameter κ = 0.017. We further demonstrate that the radiative corrections in loop diagrams are naturally suppressed by an effective cutoff Λ_eff ∼ v_H/√κ ∼ 1.9 TeV, without the need for order-by-order fine-tuning. This paper proposes testable new predictions: in the precision measurements of future Higgs factories, the Higgs couplings should exhibit characteristic deviations from the Standard Model predictions near the ∼ 2 TeV energy scale.

This paper is part of the second series (Applications and Verifications) of Space Ontology, building upon the foundational framework established in the first series (17 papers total).