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