SU(3) from the Scretching–Planck Action: Colour, Confinement, the Glueball Gap and Quarkonium Against Experiment

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].