Formalizing the SV0 Resolution of the Hierarchy Problem via the Functional Renormalization Group and Spectral Dimension Flow (Preprint)

The Hierarchy Problem—the enormous discrepancy between the electroweak scale and the Planck scale—remains a primary motivation for physics beyond the Standard Model. While the Signed-Volume (SV0) framework qualitatively addressed this via the discrete cutoff of Space Packets (Paper XIX), a rigorous renormalization group analysis is required. In this paper (Paper XXIII of the SV0 series), we formalize the SV0 resolution using the Functional Renormalization Group (FRG) approach. We demonstrate that the two-sector constraint and the discrete nature of Space Packets naturally induce a running spectral dimension d_s(k), which flows from d_s = 4 in the infrared (IR) to d_s = 2 in the ultraviolet (UV). By deriving the Wetterich equation for the Higgs scalar field within this SV0 geometry, we show that the quadratic divergences in the Higgs mass are analytically suppressed. This dynamically protects the Higgs mass from Planck-scale corrections, providing a natural and mathematically rigorous solution to the Hierarchy Problem without requiring supersymmetry or extra dimensions. References:[1] M. U. Sandaruwan, "Structurally Guaranteed Phantom Crossing in a Signed-Volume Effective Fluid..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24026844[2] M. U. Sandaruwan, "Discrete Spacetime and Space Packets..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24046352[3] M. U. Sandaruwan, "Resolution of the Hierarchy Problem and Neutrino Masses..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24049911[4] M. U. Sandaruwan, "Formalizing the SV0 Action Principle and Deformed Lorentz-Invariant Quantum Geometry..." (2026). Zenodo: https://doi.org/10.5281/zenodo.24070397