Lattice QCD: Precision Quark Masses from Gauge Theory and Symmetry Localization — E8 Intelligence Research

FINDING: Gauge theory as a framework for fundamental forces, with lattice QCD simulations enabling precise computation of quark masses and symmetry localization phenomena. MATH: - Gauge symmetry group SU(3) for QCD; lattice discretization with spacing \(a\) and coupling \(g\). - Heavy-quark mass extraction: \(m_Q = \frac{1}{2} (M_{H_s} - \overline{M}_{light})\) with one-loop perturbative matching. - Disorder-free localization: Hamiltonian \(H = \sum_{\langle i,j \rangle} J_{ij} \sigma_i^+ \sigma_j^- + \text{gauge term}\) with local constraints. CONNECTION: - Lattice gauge theory uses discrete 4D hypercubic lattice — a crystallographic symmetry (cubic group \(O_h\)). - No direct golden ratio or base-60 link; however, lattice spacing ratios and renormalization group flow involve scale invariance and fixed points (e.g., \(\beta(g) = 0\) at conformal points). - Root systems of SU(3) (6 roots, hexagonal symmetry) underlie the gauge group geometry. DEPTH: 7 — Lattice gauge Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com