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: \(m_Q = \frac{1}{2}(M_{H_s} - \bar{m}_s) + \delta m_{1\text{-loop}}\), where \(\delta m_{1\text{-loop}}\) is computed in lattice perturbation theory with the Fermilab clover action; the one-loop coefficient depends on the renormalization scheme (e.g., \(\overline{\text{MS}}\) vs. pole mass), introducing scheme dependence \(\propto \alpha_s/(4\pi) \times C_F \times (\text{log terms})\). Key constants: \(\alpha_s(M_Z) \approx 0.118\), \(C_F = 4/3\). The lattice spacing \(a\) enters via \(am_Q\), with continuum limit \(a \to 0\). | 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