F Glueball Mass Gap: Multi- CFN-Frame Mechanism on the SU(2) Wilson Lattice
Description
Title: F$_2$ Glueball Mass Gap: Multi-$\beta$ CFN-Frame Mechanism on the SU(2) Wilson Lattice
Author: Alexander Novickis (alex.novickis@gmail.com)
We report the v5 retrofit of Paper CXVIII following the post-publication audit (resolved-#12505, 2026-05-14) that demoted the v4 single-time-slice value $m_{0^{++}}^{\rm latt}(\beta = 8, L = 18) = 3.512 \pm 0.350$ from a glueball-mass extraction to a UV-scale spectral first moment of the unsmeared spatial-plaquette operator. The Option B retrofit (resolved-#12512) re-frames v5 around production-grade CFN Path-D observables on the same SU(2) Wilson lattice action, and reports the F$_2$-CFN frame mechanism claim rather than a continuum glueball-mass value. The multi-$\beta$ campaign on the rm2 cluster (3 dedicated single-seed jobs at $\beta \in \{6, 10\}$ plus three independent seeds at $\beta = 8$, all at $L = 18$) yields the equal-time Path-D observables $\langle |X|\rangle$ (off-diagonal-field norm) and $\langle |\hat n|\rangle$ (colour-direction-field norm) stable to four decimal places across the $\beta$-scan window: $\langle |X|\rangle = 0.9487 \pm 0.0001$ and $\langle |\hat n|\rangle = 0.1098 \pm 0.0001$ for $\beta \in \{6, 8, 10\}$. The X-mass-dominance pattern (~94.9% of link content in the off-diagonal sector, ~11.0% in the colour-direction sector) is therefore a robust frame fingerprint of heatbath-thermalised SU(2) Wilson configurations, independent of lattice spacing across nearly a factor of two in $a$. v5 establishes the existence claim: the F$_2$-CFN frame decomposition is numerically realised on production-grade SU(2) Wilson configurations and the X-dominance pattern is stable across the scaling window. v5 does not claim a continuum-extrapolated $m_{0^{++}}$ value; that quantitative deliverable is queued for v6 (multi-operator GEVP + Wilson-loop string tension + universal-ratio Symanzik fit against the Teper SU(2) benchmark $m_{0^{++}}/\sqrt{\sigma} = 3.74 \pm 0.12$). The v4 single-slice number 3.512 is preserved as a UV-scale diagnostic only; the previous "1.71 GeV agreement" narrative is retracted.
Key results include:
- v5 reframes CXVIII around the F$_2$-CFN frame mechanism, not a glueball-mass value. The v4 single-slice 3.512 number is demoted to a UV-scale diagnostic (audit #12505).
- Multi-$\beta$ CFN Path-D observables harvested from rm2 (5 production jobs, $\beta \in \{6, 8, 10\}$, $L = 18$) confirm $\langle |X|\rangle \approx 0.949$ and $\langle |\hat n|\rangle \approx 0.110$ stable to 4 decimal places across the scan window.
- X-mass dominance is the frame fingerprint of heatbath-thermalised SU(2) Wilson configurations; ~94.9% of link content in the off-diagonal sector is invariant to lattice spacing.
- No continuum glueball-mass extraction: that is the v6 (Option A) scope; needs multi-operator GEVP + Wilson-loop $\sigma$ + universal-ratio Symanzik fit against Teper SU(2) 3.74.
- CLIX §6.4 v14 (1.729 GeV) + lattice QCD (1.71-1.74 GeV) still agree on the $0^{++}$ value; CXVIII v5 contributes the mechanism, not the value (see §4).
- v5.1 (2026-06-02): finite-volume systematic now measured. A companion L-scan at the central coupling $\beta_{\rm nom}=8$ ($L = 18/20/24$, identical plaquette to five decimals) replaces the earlier external estimate with a direct measurement: the X-dominance observables vary by only $\Delta\langle |X|\rangle \approx 1.4\times10^{-3}$ ($\sim$0.14%) and $\Delta\langle |\hat n|\rangle \approx 3\times10^{-4}$ ($\sim$0.3%) across the three volumes, with no monotone drift (§7.2). The single-slice glueball estimator is volume-stable for $L \ge 20$ ($2.92$ vs. $3.01$), consistent with the no-continuum-mass conclusion.
Keywords: [physics, QCD, glueball, mass gap, Yang-Mills, SU(2), Wilson lattice, lattice gauge theory, CFN decomposition, Cho-Faddeev-Niemi, flag manifold, color-direction field, monopole, Abelian dominance, heatbath, Kennedy-Pendleton, finite-volume systematic, finite-size scaling, plaquette, string tension, GEVP, Symanzik improvement, Teper benchmark, continuum extrapolation, Hopf soliton, F2, topological soliton]
Series: Paper CXVIII in the Hopf Soliton Programme