Paper V Glueball Harmonics and the Yang-Mills Mass Gap: A Physical Derivation from QCD Confinement Geometry
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2026
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| _version_ | 1866901461956296704 |
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| author | Schulz, Matthew |
| author_facet | Schulz, Matthew |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19847429 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Paper V Glueball Harmonics and the Yang-Mills Mass Gap: A Physical Derivation from QCD Confinement Geometry Schulz, Matthew glueball · Yang-Mills mass gap · MIT bag model · Bessel zeros · N_c expansion · pion harmonics · J/ψ · Υ · QCD · PDG 2025 Abstract <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> |
| title | Paper V Glueball Harmonics and the Yang-Mills Mass Gap: A Physical Derivation from QCD Confinement Geometry |
| topic | glueball · Yang-Mills mass gap · MIT bag model · Bessel zeros · N_c expansion · pion harmonics · J/ψ · Υ · QCD · PDG 2025 Abstract |
| url | https://doi.org/10.5281/zenodo.19847429 |