Meson and baryon masses from $G_2$ octonion algebra
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2026
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| _version_ | 1866901223817347072 |
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| author | Liebmann, Manfred |
| author_facet | Liebmann, Manfred |
| contents | <p>Starting from the octonionic Dirac equation on $\mathrm{Cl}(0,7)$ developed in the companion paper, we derive the complete pseudoscalar meson octet ($\pi$, $K$, $\eta$) and the baryon octet and decuplet from the $G_2$ tensor representations $\Lambda^2_{\mathbf{7}}$ and $\Lambda^3_{\mathbf{1}} \oplus \Lambda^3_{\mathbf{7}} \oplus \Lambda^3_{\mathbf{27}}$. The only input is the Planck mass~$M_P$; the gauge group~$G_2 = \mathrm{Aut}(\mathbb{O})$ and its Lie algebra determine the gauge coupling $g^2 = 3/7$ (Killing form), the electroweak scale $\kappa = 122.8\,\mathrm{GeV}$ (BCS gap equation), and all mass ratios through the integers labelling $G_2$ representations. For rank-even composites (mesons) the mass shift enters as~$m^2$; for rank-odd composites (baryons) it enters as~$m$. The pion mass is predicted to be $m_\pi = 141\,\mathrm{MeV}$ (experiment: $140\,\mathrm{MeV}$, deviation~$0.7\%$). For the full baryon octet and decuplet the mean absolute deviation is~$1.2\%$ with \emph{no free parameters}.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19418520 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Meson and baryon masses from $G_2$ octonion algebra Liebmann, Manfred octonions; G2 gauge theory; meson masses; baryon masses; Gell-Mann-Okubo formula; pseudoscalar mesons; baryon octet; baryon decuplet; eta-eta prime mixing; strangeness <p>Starting from the octonionic Dirac equation on $\mathrm{Cl}(0,7)$ developed in the companion paper, we derive the complete pseudoscalar meson octet ($\pi$, $K$, $\eta$) and the baryon octet and decuplet from the $G_2$ tensor representations $\Lambda^2_{\mathbf{7}}$ and $\Lambda^3_{\mathbf{1}} \oplus \Lambda^3_{\mathbf{7}} \oplus \Lambda^3_{\mathbf{27}}$. The only input is the Planck mass~$M_P$; the gauge group~$G_2 = \mathrm{Aut}(\mathbb{O})$ and its Lie algebra determine the gauge coupling $g^2 = 3/7$ (Killing form), the electroweak scale $\kappa = 122.8\,\mathrm{GeV}$ (BCS gap equation), and all mass ratios through the integers labelling $G_2$ representations. For rank-even composites (mesons) the mass shift enters as~$m^2$; for rank-odd composites (baryons) it enters as~$m$. The pion mass is predicted to be $m_\pi = 141\,\mathrm{MeV}$ (experiment: $140\,\mathrm{MeV}$, deviation~$0.7\%$). For the full baryon octet and decuplet the mean absolute deviation is~$1.2\%$ with \emph{no free parameters}.</p> |
| title | Meson and baryon masses from $G_2$ octonion algebra |
| topic | octonions; G2 gauge theory; meson masses; baryon masses; Gell-Mann-Okubo formula; pseudoscalar mesons; baryon octet; baryon decuplet; eta-eta prime mixing; strangeness |
| url | https://doi.org/10.5281/zenodo.19418520 |