Paper XLIX: The Strong Coupling Constant from Kaluza-Klein Beta Functions
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2026
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| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <div> <h4>Abstract</h4> <p>The strong coupling constant $\alpha_s(M_Z) = 0.1180 \pm 0.0009$ is among the least precisely known of the Standard Model parameters. We derive it from the Kaluza-Klein spectrum on $S^3_\lambda \times S^7$, the compact space of the topological soliton framework. The Berger sphere $S^3_\lambda$ with squashing parameter $\lambda = \sqrt{2}$ (selected by the horizontal Ricci-flat condition, Paper VII) determines the KK mass gaps and mode degeneracies. The SU(3) color gauge group is embedded in the SO(8) isometry of $S^7$ via the canonical $\text{SU}(3) \subset \text{SU}(4) \subset \text{SO}(8)$ chain. Above the compactification scale $M_\text{KK} \sim 10^{17}$ GeV, the gauge coupling runs with a power law $\alpha_s^{-1}(\mu) \propto \mu^3$ due to the cubic growth of KK mode degeneracies in $d = 7$ extra dimensions. Below $M_\text{KK}$, the running transitions to the standard logarithmic form with $b_0 = 7$ (pure SU(3), six quark flavors). Matching at $M_\text{KK}$ with the geometric coupling $\alpha_\text{GUT} = 1/44$ determines the strong coupling at all lower scales. The two-loop evolution from $M_\text{KK}$ to $M_Z$ yields $\alpha_s(M_Z) = 0.1183$, within the PDG uncertainty band. At the intermediate Hopf scale $F = 255$ GeV: $\alpha_s(F) = 0.095$, which served as the input for the $f_\pi = 92.1$ MeV derivation in Paper XLIV. The power-law running above $M_\text{KK}$ provides the first mechanism in this series for the rapid convergence of all three gauge couplings, replacing the MSSM requirement of low-energy supersymmetry with the geometry of the internal manifold.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>topology</span> <span>solitons</span> <span>QCD</span> <span>strong coupling</span> <span>kaluza klein</span> <span>running couplings</span> <span>unification</span> <span>berger sphere</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-04-05</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19349074">10.5281/zenodo.19349074</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
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| spellingShingle | Paper XLIX: The Strong Coupling Constant from Kaluza-Klein Beta Functions Novickis, Alexander physics topology solitons QCD strong-coupling kaluza-klein running-couplings unification berger-sphere <div> <h4>Abstract</h4> <p>The strong coupling constant $\alpha_s(M_Z) = 0.1180 \pm 0.0009$ is among the least precisely known of the Standard Model parameters. We derive it from the Kaluza-Klein spectrum on $S^3_\lambda \times S^7$, the compact space of the topological soliton framework. The Berger sphere $S^3_\lambda$ with squashing parameter $\lambda = \sqrt{2}$ (selected by the horizontal Ricci-flat condition, Paper VII) determines the KK mass gaps and mode degeneracies. The SU(3) color gauge group is embedded in the SO(8) isometry of $S^7$ via the canonical $\text{SU}(3) \subset \text{SU}(4) \subset \text{SO}(8)$ chain. Above the compactification scale $M_\text{KK} \sim 10^{17}$ GeV, the gauge coupling runs with a power law $\alpha_s^{-1}(\mu) \propto \mu^3$ due to the cubic growth of KK mode degeneracies in $d = 7$ extra dimensions. Below $M_\text{KK}$, the running transitions to the standard logarithmic form with $b_0 = 7$ (pure SU(3), six quark flavors). Matching at $M_\text{KK}$ with the geometric coupling $\alpha_\text{GUT} = 1/44$ determines the strong coupling at all lower scales. The two-loop evolution from $M_\text{KK}$ to $M_Z$ yields $\alpha_s(M_Z) = 0.1183$, within the PDG uncertainty band. At the intermediate Hopf scale $F = 255$ GeV: $\alpha_s(F) = 0.095$, which served as the input for the $f_\pi = 92.1$ MeV derivation in Paper XLIV. The power-law running above $M_\text{KK}$ provides the first mechanism in this series for the rapid convergence of all three gauge couplings, replacing the MSSM requirement of low-energy supersymmetry with the geometry of the internal manifold.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>topology</span> <span>solitons</span> <span>QCD</span> <span>strong coupling</span> <span>kaluza klein</span> <span>running couplings</span> <span>unification</span> <span>berger sphere</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-04-05</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19349074">10.5281/zenodo.19349074</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| title | Paper XLIX: The Strong Coupling Constant from Kaluza-Klein Beta Functions |
| topic | physics topology solitons QCD strong-coupling kaluza-klein running-couplings unification berger-sphere |
| url | https://doi.org/10.5281/zenodo.19434797 |