Lattice Gauge Theory Enables Non-Perturbative QCD Mass Calculations — E8 Intelligence Research

FINDING: Lattice gauge theory computationally discretizes continuous gauge fields onto a spacetime grid, enabling non-perturbative QCD calculations (e.g., heavy-quark masses) via path-integral Monte Carlo. | MATH: Wilson action \\( S_G = \\beta \\sum_{\\text{plaquettes}} \\left(1 - \\frac{1}{N_c} \\text{Re Tr}\\, U_{\\mu\\nu} \\right) \\), with \\( \\beta = 2N_c/g^2 \\); quark masses extracted from meson correlators \\( C(t) \\propto e^{-m_H t} \\); Fermilab method uses clover-improved Wilson fermions with \\( O(a) \\) improvement coefficient \\( c_{SW} \\). | CONNECTION: The lattice itself is a hypercubic grid — a 4D crystallographic lattice with \\( D_4 \\) (hypercubic) root system symmetry. The plaquette term embodies the smallest Wilson loop, a discrete holonomy — a geometric parallel transport around a unit square, echoing the curvature 2-form \\( F_{\\mu\\nu} \\) in the continuum limit \\( a \\to 0 \\). The ratio \\( m_H / \\Lambda_{\\text{QCD}} \\) is scale-invariant; no golden-ratio constants appear in the cited Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com