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

Abstract

**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 \( U_\mu(x) = e^{i a A_\mu(x)} \) replace continuous fields. - Heavy-quark mass \( m_Q \) extracted from meson masses: \( M_{\text{meson}} = m_Q + \bar{\Lambda} + O(1/m_Q) \), with one-loop perturbative matching. - Fermilab action: \( S = \sum_x \bar{\psi}_x (m_0 + \gamma_0 \nabla_0 + \sum_i \gamma_i \nabla_i - \frac{a}{2} \sum_i \nabla_i^2) \psi_x \). **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