Lattice Gauge Theory: Non-Perturbative Framework for Extracting Heavy-Quark Masses — E8 Intelligence Research

FINDING: Lattice gauge theory provides a non-perturbative, discrete computational framework for quantum field theories (QCD, electromagnetism), enabling numerical extraction of fundamental parameters like heavy-quark masses via lattice perturbation theory. | MATH: Lattice regularization replaces continuous spacetime with a hypercubic lattice (spacing \\(a\\)); gauge fields \\(U_\\mu(x) = e^{i a g A_\\mu(x)}\\) (link variables, \\(SU(3)\\) for QCD); Wilson action \\(S_W = \\beta \\sum_{\\text{plaquettes}} \\left(1 - \\frac{1}{N} \\text{Re Tr}\\, U_P \\right)\\), \\(\\beta = 2N/g^2\\); heavy-quark mass extraction via meson mass combinations \\(M_{H_s} = m_h + m_s + E_{\\text{binding}}\\) with one-loop lattice perturbation theory corrections (arXiv:0710.4339). | CONNECTION: The hypercubic lattice is a discrete subgroup of the Euclidean group — its symmetry group is the hyperoctahedral group \\(B_4\\) (order 384), a crystallographic point group. The plaquette action embodies the smallest closed loop (square) — a 4- Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com