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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19847429 |
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Table of Contents:
- <p>Paper V in the Harmonic Structure of the Standard Model series</p> <p>Abstract<br>We extend the pion harmonic framework (Papers I–IV, PDG 2025) to the glueball<br>sector and derive the Yang-Mills mass gap as Δ = Nc²(x₁/π)mπ = 1737.5 MeV (lattice:<br>1730 ± 100 MeV, deviation 0.43%). The derivation proceeds from the gluon<br>Neumann boundary condition j₁(kR) = 0 in a spherical bag of radius R_g = π×Rπ/Nc²<br>= 0.5103 fm. The full glueball spectrum M(J^PC) = x_{l,n}×ℏc/R_g is predicted, with<br>the 0++ (0.43%), 2++ (6.8%), and 1+− (1.6%) states passing to within lattice<br>uncertainties. The QCD string tension σ = π²mπ² = 0.17981 GeV² (PDG 2025 lattice:<br>0.18 ± 0.01 GeV², deviation 0.10%) provides independent confirmation. We do not<br>claim a solution to the Clay Millennium Problem; the physical derivation gives the<br>value and mechanism of the mass gap but is not a rigorous existence proof for the<br>quantum Yang-Mills theory on ℝ⁴.</p>