SU(3) from the Scretching–Planck Action: Colour, Confinement, the Glueball Gap and Quarkonium Against Experiment
Year: 2026
Type: preprint
Abstract: This study formulates the color dynamics of Scretching–Planck (SP) quark triplets using local \(SU(3)\) gauge symmetry and the Yang–Mills kinetic term for eight self-interacting gluon fields. In pure \(SU(3)\) lattice gauge theory, the study estimates the vacuum-weighted gap \(\Delta=(g^2/2a)\lambda(P_0)\) at three lattice spacings. The estimates are positive at all three spacings, and the continuum extrapolation gives \(\Delta/\sqrt{\sigma}=3.90\pm0.57\), consistent with the literature value \(3.64(9)\). Seven applications cover color factors, asymptotic freedom and four-loop running, the hadronic \(R\) ratio at four energies, quarkonium spectroscopy, the relation between string tension and Regge slope, confinement, and neutral-pion decay. The \(SU(3)\) color factors \(C_A=3\) and \(C_F=4/3\) are compared with LEP values \(2.89(21)\) and \(1.30(9)\). Four-loop running gives \(\alpha_s(m_\tau)=0.319\), compared with \(0.328(13)\). The Cornell-potential calculation gives an RMS deviation of \(11.2\) MeV across eight quarkonium levels. The calculated Regge slope is \(0.881\ \mathrm{GeV}^{-2}\), compared with approximately \(0.88\ \mathrm{GeV}^{-2}\), and the calculated \(\pi^0\to\gamma\gamma\) width is \(7.78\) eV, compared with \(7.80(12)\) eV. The continuum gap estimate is numerical, and a rigorous positive lower bound remains open [1–57].
Author: Scretching, Daniel
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225399247