QCD Lattice Tests Refute Golden-Ratio Meson Mass Hypothesis — E8 Intelligence Research

Abstract

FINDING: Lattice QCD and perturbative QCD methods for meson masses and parton distributions show no direct golden-ratio correction; the φ-commensurability hypothesis for particle mass seeds is explicitly challenged. | MATH: Lattice QCD uses Euclidean path integrals, quark mass renormalization via one-loop lattice perturbation theory (e.g., Fermilab method: \(m_q = Z_m m_0\), \(Z_m = 1 + \alpha_s C_F/(4\pi) \ln(a\mu) + \dots\)); meson mass ratios from lattice spectra (e.g., \(m_{D_s}/m_{J/\psi}\), \(m_{\pi}/m_{\rho}\)) are computed numerically, not via φ. Parton distribution functions extracted via quasi-PDFs: \(\tilde{q}(x, P_z) = \int dz e^{ixP_z z} \langle P | \bar\psi(z) \gamma^z \psi(0) | P \rangle\), matched to light-cone PDFs via perturbative matching kernels. | CONNECTION: No geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) appears in these QCD results. Lattice QCD does use crystallographic-like discrete symmetry groups (hypercubic lattice, \(H(4)\) symmetry, root system \( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com