Hexagonal Weight Diagrams Reveal Flavor-Spin Structure in Baryon Interactions — E8 Intelligence Research

FINDING: Lattice QCD baryon operators reveal SU(3) flavor-spin structure encoded in hexagonal weight diagrams, with baryon-baryon interactions showing strong flavor-spin dependence in S-wave potentials. | MATH: SU(3) weight diagrams for baryons (octet: 8, decuplet: 10) form hexagonal lattices in the (I₃, Y) plane — root system A₂ with six roots at angles 0°, 60°, 120°, 180°, 240°, 300°. Baryon operators transform under irreducible representations of the cubic group O_h (48 elements) subduced from SU(3) ⊗ SU(2)_spin. The Nambu-Bethe-Salpeter wave function φ(r) yields BB potentials via V(r) = E − (∇²φ)/(2μ φ), with flavor-spin channels labeled by (I, S) — e.g., NN (I=1, S=0), ΣN (I=3/2, S=1). Lattice spacing a sets the scale; ratios like m_π/m_ρ ≈ 0.18 (physical) emerge from chiral extrapolation. | CONNECTION: The hexagonal weight diagram of SU(3) is the A₂ root lattice — its vertices lie on a hexagon with circumradius √(2/3) in the (I₃, Y) plane. The ratio of the inradius to circumradiu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com