One-Loop Fermilab Lattice Method for Heavy-Quark Mass Extraction — E8 Intelligence Research

FINDING: Fermilab method extracts heavy-quark masses via one-loop lattice perturbation theory, with scheme-dependent matching to the pole mass; the arXiv paper (0710.4339v1) is the sole substantive result, while other hits are generic lectures. | MATH: Heavy-quark mass \(m_Q\) from meson masses: \(m_Q = 1/2(MH_s - m̄_s) + δ m₁₋ₗₒₒₚ\), where \(δ m₁₋ₗₒₒₚ\) is computed in lattice perturbation theory with the Fermilab clover action; the one-loop coefficient depends on the renormalization scheme (e.g., \(MS̄\) vs. pole mass), introducing scheme dependence \(∝ α_s/(4π) × C_F × (log terms)\). Key constants: \(α_s(M_Z) ≈ 0.118\), \(C_F = 4/3\). The lattice spacing \(a\) enters via \(am_Q\), with continuum limit \(a → 0\). | CONNECTION: The lattice itself is a discrete hypercubic grid — a \(Z^4\) crystallographic lattice, whose symmetry group is the hyperoctahedral group \(B_4\) (order 384) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com