F₂ Glueball Mass Gap: Multi-β CFN-Frame Mechanism on the SU(2) Wilson Lattice
Description
We study pure SU(2) lattice gauge theory through the Cho–Faddeev–Niemi (CFN) decomposition of the link variables, and report a numerical mechanism result on standard SU(2) Wilson configurations. On heatbath-thermalised configurations we measure the equal-time Path-D observables ⟨ |X|⟩ (off-diagonal-field norm) and ⟨ |n|⟩ (colour-direction-field norm). Across a ten-point coupling scan (nominal β ∈ {4,…,20} at L = 18, spanning a factor ~ 4 in lattice spacing) these are stable to ~ 10⁻⁴: ⟨ |X|⟩ = 0.9487 ± 0.0001 and ⟨ |n|⟩ = 0.1098 ± 0.0001, so ~ 94.9% of the link content sits in the off-diagonal X sector and ~ 11.0% in the colour-direction n sector. This X-dominance pattern is a robust frame fingerprint of thermalised SU(2) Wilson configurations, essentially independent of lattice spacing. The result is an existence/mechanism claim — the F₂-CFN frame decomposition is numerically realised and stable — not a continuum glueball-mass extraction. The single-slice effective mass of the unsmeared scalar operator is a UV-scale diagnostic (it tracks the lattice cutoff rather than decreasing with a); a continuum m_0⁺⁺ requires a smeared multi-operator GEVP, the Wilson-loop string tension, and a universal-ratio Symanzik fit, which are not performed here. The programme's analytical glueball mass (Paper CLIX, m_0⁺⁺ = 1.729 GeV) and external lattice QCD (1.71–1.74 GeV) supply the value; this paper supplies the mechanism.
Files
F2_Glueball_Mass_Gap.pdf
Additional details
References
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