Geometric Regularization of the Standard Model Yukawa Hierarchy: Mass-to-Radius Cavity Scaling in Local Interaction Field Equilibrium

Abstract

The Standard Model of particle physics successfully classifies elementary fermions but introduces nineteen arbitrary empirical parameters, dominated by the unexplained span of Yukawa coupling constants spanning six orders of magnitude between the electron () and the top quark (). In this paper, we demonstrate that the Yukawa hierarchy problem is an artifact of treating elementary fermions as point-like particles coupled to an abstract scalar vacuum expectation value. Within the framework of Local Interaction Field Equilibrium (LIFE), we prove that elementary particles are stable, three-dimensional electromagnetic cavity eigenmodes governed by the master volumetric force-density balance (). By equating the Standard Model mass formulation with the 3D spherical cavity quantization spectrum (), we derive an exact analytical expression for the effective Yukawa coupling: . This establishes that the Yukawa coupling is not an arbitrary fundamental constant of nature, but a geometric scaling parameter inversely proportional to the physical cavity radius  (). The minute electron coupling emerges naturally from its extended picometer cavity (), whereas heavy fermions (tauon, top quark) achieve couplings of order unity because non-linear gravito-inertial self-compression (Term B-6: ) forces them into ultra-compact femtometer enclosures (). This completely resolves the Yukawa hierarchy problem without requiring supersymmetry, extra dimensions, or Froggatt-Nielsen flavor symmetries.

Keywords: Local Interaction Field Equilibrium (LIFE Theory); Standard Model Hierarchy; Yukawa Couplings; Spherical Bessel Cavity Quantization; Gravito-Inertial Compaction; Electroweak Scale.