Lattice Gauge Theory for Heavy-Quark Mass via Fermilab Method and Perturbation — E8 Intelligence Research

**FINDING:** Lattice gauge theory discretizes spacetime to compute non-perturbative quantum field dynamics, with heavy-quark mass calculations using Fermilab method and one-loop perturbation theory. **MATH:** - Lattice spacing \( a \) defines UV cutoff; gauge links \( U_μ(x) = ei a A_μ(x) \) replace continuous fields. - Heavy-quark mass \( m_Q \) extracted from meson masses: \( Mₘₑₛₒₙ = m_Q + Λ̄ + O(1/m_Q) \), with one-loop perturbative matching. - Fermilab action: \( S = ∑_x ψ̄_x (m_0 + γ_0 ∇_0 + ∑_i γ_i ∇_i - a/2 ∑_i ∇_i^2) ψ_x \). **CONNECTION:** - Lattice discretization inherently ties to **root systems** (e.g., \( A_3 \) for cubic lattice) and **crystallographic symmetry** (hypercubic group \( BC_4 \)). - No explicit golden ratio or base-60 ratios appear; lattice spacing \( a \) is a free parameter, not a fixed geometric ratio. **DEPTH:** 6 — Lattice gauge theory is a foundational comp Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com