Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2025
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| Online-Zugang: | https://doi.org/10.5281/zenodo.17619696 |
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Inhaltsangabe:
- <p>The apparent near-unification of the three Standard-Model (SM) gauge couplings has long intrigued physicists. While supersymmetric or grand-unified theories (SUSY/GUT) achieve precise convergence through additional particles or symmetries, the SM itself seems to approach—but not quite reach—unification. This raises a fundamental question: could the near-merging of <span><span>α1\alpha_1</span><span><span><span><span>α</span><span><span><span><span><span><span>1</span></span></span><span></span></span></span></span></span></span></span></span>, <span><span>α2\alpha_2</span><span><span><span><span>α</span><span><span><span><span><span><span>2</span></span></span><span></span></span></span></span></span></span></span></span>, and <span><span>α3\alpha_3</span><span><span><span><span>α</span><span><span><span><span><span><span>3</span></span></span><span></span></span></span></span></span></span></span></span> arise naturally from the internal geometry of the SM’s renormalization group (RG) flow, without invoking new physics?</p> <p>In this work, we approach the problem from an <strong>information-geometric perspective</strong>. We treat the evolution of gauge couplings as a trajectory on a statistical manifold and define a dynamical cost functional</p> <p><span><span><span>F=R+αdyn τ2,F = \mathcal{R} + \alpha_{\rm dyn}\,\tau^2,</span><span><span><span>F</span><span>=</span></span><span><span>R</span><span>+</span></span><span><span><span>α</span><span><span><span><span><span><span><span>dyn</span></span></span></span><span></span></span></span></span></span><span><span>τ</span><span><span><span><span><span><span>2</span></span></span></span></span></span></span><span>,</span></span></span></span></span></p> <p>where <span><span>R\mathcal{R}</span><span><span><span>R</span></span></span></span> measures curvature (bending of the flow) and <span><span>τ\tau</span><span><span><span>τ</span></span></span></span> quantifies shear (differential tilt between sectors). The parameter <span><span>αdyn\alpha_{\rm dyn}</span><span><span><span><span>α</span><span><span><span><span><span><span><span>dyn</span></span></span></span><span></span></span></span></span></span></span></span></span> plays the role of a shear modulus, balancing curvature and deformation, analogous to elastic stability in continuum mechanics.</p> <p>Using this formulation, we discover a <strong>dynamostatic plateau</strong>—a finite, window-locked interval where the informational action-rate <span><span>FF</span><span><span><span>F</span></span></span></span> becomes stationary (<span><span>dF/dL≃0dF/dL \simeq 0</span><span><span><span>d</span><span>F</span><span>/</span><span>d</span><span>L</span><span>≃</span></span><span><span>0</span></span></span></span>). Remarkably, this plateau aligns precisely with the SM’s empirical RG crossings, <span><span>L13L_{13}</span><span><span><span><span>L</span><span><span><span><span><span><span>13</span></span></span><span></span></span></span></span></span></span></span></span> and <span><span>L12L_{12}</span><span><span><span><span>L</span><span><span><span><span><span><span>12</span></span></span><span></span></span></span></span></span></span></span></span>, and encloses the minimum of the coupling spread (RMS). The effect is robust across smoothing scales, tolerance thresholds, and variations in <span><span>αdyn\alpha_{\rm dyn}</span><span><span><span><span>α</span><span><span><span><span><span><span><span>dyn</span></span></span></span><span></span></span></span></span></span></span></span></span>.</p> <p>This result suggests that the SM’s near-unification is not accidental, but an emergent feature of its <strong>informational geometry</strong>—a regime of minimal organizational cost where curvature and shear co-balance. The phenomenon, which we term <strong>information-geometric dynamostasis</strong>, provides a falsifiable, model-minimal explanation of coupling concordance, offering an alternative to supersymmetric unification and pointing toward a deeper geometric order underlying the SM itself.</p>