Lattice QCD Extraction of Heavy-Quark Masses via One-Loop Perturbative Matching — E8 Intelligence Research

FINDING: Fermilab method extracts heavy-quark masses via one-loop lattice perturbation theory, combining lattice QCD with automated perturbative matching to control scheme dependence. | MATH: Heavy-quark mass \\( m_Q \\) from lattice-determined heavy-strange meson mass \\( M_{H_s} \\) via \\( m_Q = M_{H_s} - \\bar{\\Lambda} + \\delta m_{\\text{1-loop}} \\); one-loop matching coefficient \\( C_1(\\mu) \\) with renormalization scale \\( \\mu \\), scheme dependence enters through \\( \\alpha_s(\\mu) \\) and lattice spacing \\( a \\) via \\( a^{-1} \\) setting. Key constants: \\( \\alpha_s(M_Z) \\approx 0.118 \\), lattice spacing \\( a \\approx 0.09–0.12 \\) fm. | CONNECTION: Lattice QCD is a discrete hypercubic lattice — a crystallographic structure with cubic symmetry (space group \\( Pm\\bar{3}m \\)), whose Brillouin zone and root system \\( B_3 \\) (or \\( A_3 \\) for staggered fermions) encode the discretized Dirac operator. The one-loop perturbative correction involves sums over lattice momenta that respect this cubic sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com