From Quarks to Neutrinos: A Fractal Framework for Elementary Particle Hierarchy

Abstract

This paper presents Unified Fractal Quantum Field Theory (UFQFT), a novel framework that reinterprets particle physics through fractal field resonances and dimensional scaling. In UFQFT, the mass spectrum of fundamental particles emerges from the fractal dimension (D) of their underlying quantum fields, governed by the scaling law m ∝ |D − 2.70|⁻ᵅ, where α distinguishes between quark (α ≈ 1.5) and lepton (α ≈ 2.0) sectors. The theory eliminates the need for gluons by explaining quark confinement via fractal binding energies and recasts the Higgs mechanism as a critical fractal phase transition of the Φ energy field. Key predictions include: (1) the composite nature of the down quark (d ≈ u ⊗ e⁻), (2) neutrino masses as residual Φ-field vibrations (D ≈ 2.72), and (3) proton stability as a consequence of fractal synchrony (Dₚ ≈ 2.66). UFQFT challenges the Standard Model by unifying electroweak and strong interactions through geometric field modulation, offering testable signatures in high-energy collisions (e.g., fractal dimension imprints at D ≈ 2.65–2.70). The model’s mathematical consistency and empirical viability are demonstrated through precise mass calculations for quarks (u, d, s, c), leptons (e⁻, νₑ), and hadrons (p, n), with deviations <1% for most particles. This work opens new pathways for beyond-Standard-Model physics by integrating fractal geometry into quantum field dynamics.