| _version_ | 1866901084728983552 |
|---|---|
| author | Bhatt, Aaditya |
| author_facet | Bhatt, Aaditya |
| contents | <p>We propose (STRONG CONJECTURE) that the strong coupling constant at the proton mass scale is determined by the Seifert monodromy period of the trefoil knot complement: <span><span><span><span><span><span>α</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>(</span><span><span>m</span><span><span><span><span><span><span><span>p</span></span></span></span><span></span></span></span></span></span><span>)</span><span>=</span></span><span><span>pq</span><span>/</span><span>(</span><span>4</span><span>π</span><span>)</span><span>=</span></span><span><span>3/</span><span>(</span><span>2</span><span>π</span><span>)</span><span>≈</span></span><span><span>0.4775</span></span></span></span></span> where <span><span><span><span><span>(</span><span>p</span><span>,</span><span>q</span><span>)</span><span>=</span></span><span><span>(</span><span>2</span><span>,</span><span>3</span><span>)</span></span></span></span></span> are the torus knot parameters. This equals <span><span><span><span><span><span>N</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>/</span><span>(</span><span>2</span><span>π</span><span>)</span></span></span></span></span> where <span><span><span><span><span><span>N</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>q</span><span>=</span></span><span><span>3</span></span></span></span></span> is the number of QCD colours. Standard 2-3-loop QCD running with threshold matching brackets the PDG 2024 world average <span><span><span><span><span>0.1180</span><span>±</span></span><span><span>0.0009</span></span></span></span></span> between +0.60 (2-loop) and -0.70 (3-loop); four-loop running yields <span><span><span><span><span>≈</span></span><span><span>0.1179</span></span></span></span></span> (0.10).</p> <p>We further observe that the one-loop <span><span><span><span><span>β</span></span></span></span></span>-function coefficient <span><span><span><span><span><span>b</span><span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>(</span><span>33</span><span>−</span></span><span><span>2</span><span><span>n</span><span><span><span><span><span><span><span>f</span></span></span></span><span></span></span></span></span></span><span>)</span><span>/</span><span>(</span><span>12</span><span>π</span><span>)</span><span>=</span></span><span><span>9/</span><span>(</span><span>4</span><span>π</span><span>)</span></span></span></span></span> for <span><span><span><span><span><span>n</span><span><span><span><span><span><span><span>f</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>3</span></span></span></span></span> decomposes exactly and algebraically into orbifold contributions from the Seifert base <span><span><span><span><span><span>D</span><span><span><span><span><span><span><span>2</span></span></span></span></span></span></span></span><span>(</span><span>2</span><span>,</span><span>3</span><span>)</span></span></span></span></span>.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19286317 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Strong Coupling Constant from Seifert Monodromy and Orbifold Geometry of the Trefoil Knot Complement Bhatt, Aaditya Strong Coupling Constant Quantum Chromodynamics (QCD) Seifert Monodromy Orbifold Geometry Trefoil Knot Discrete Topological Torsion Theory (DTTT) Beta Function <p>We propose (STRONG CONJECTURE) that the strong coupling constant at the proton mass scale is determined by the Seifert monodromy period of the trefoil knot complement: <span><span><span><span><span><span>α</span><span><span><span><span><span><span><span>s</span></span></span></span><span></span></span></span></span></span><span>(</span><span><span>m</span><span><span><span><span><span><span><span>p</span></span></span></span><span></span></span></span></span></span><span>)</span><span>=</span></span><span><span>pq</span><span>/</span><span>(</span><span>4</span><span>π</span><span>)</span><span>=</span></span><span><span>3/</span><span>(</span><span>2</span><span>π</span><span>)</span><span>≈</span></span><span><span>0.4775</span></span></span></span></span> where <span><span><span><span><span>(</span><span>p</span><span>,</span><span>q</span><span>)</span><span>=</span></span><span><span>(</span><span>2</span><span>,</span><span>3</span><span>)</span></span></span></span></span> are the torus knot parameters. This equals <span><span><span><span><span><span>N</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>/</span><span>(</span><span>2</span><span>π</span><span>)</span></span></span></span></span> where <span><span><span><span><span><span>N</span><span><span><span><span><span><span><span>c</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>q</span><span>=</span></span><span><span>3</span></span></span></span></span> is the number of QCD colours. Standard 2-3-loop QCD running with threshold matching brackets the PDG 2024 world average <span><span><span><span><span>0.1180</span><span>±</span></span><span><span>0.0009</span></span></span></span></span> between +0.60 (2-loop) and -0.70 (3-loop); four-loop running yields <span><span><span><span><span>≈</span></span><span><span>0.1179</span></span></span></span></span> (0.10).</p> <p>We further observe that the one-loop <span><span><span><span><span>β</span></span></span></span></span>-function coefficient <span><span><span><span><span><span>b</span><span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>(</span><span>33</span><span>−</span></span><span><span>2</span><span><span>n</span><span><span><span><span><span><span><span>f</span></span></span></span><span></span></span></span></span></span><span>)</span><span>/</span><span>(</span><span>12</span><span>π</span><span>)</span><span>=</span></span><span><span>9/</span><span>(</span><span>4</span><span>π</span><span>)</span></span></span></span></span> for <span><span><span><span><span><span>n</span><span><span><span><span><span><span><span>f</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>3</span></span></span></span></span> decomposes exactly and algebraically into orbifold contributions from the Seifert base <span><span><span><span><span><span>D</span><span><span><span><span><span><span><span>2</span></span></span></span></span></span></span></span><span>(</span><span>2</span><span>,</span><span>3</span><span>)</span></span></span></span></span>.</p> |
| title | The Strong Coupling Constant from Seifert Monodromy and Orbifold Geometry of the Trefoil Knot Complement |
| topic | Strong Coupling Constant Quantum Chromodynamics (QCD) Seifert Monodromy Orbifold Geometry Trefoil Knot Discrete Topological Torsion Theory (DTTT) Beta Function |
| url | https://doi.org/10.5281/zenodo.19286317 |