Light-quark hadron spectroscopy: A geometric quark model forSstates

Abstract

A geometric light-quark model is described in which all quark-quark binding energies are less than 5%. The quark states of this model are formed entirely from a single mass quantum $M$, which has the same principal quantum numbers as the kaon. $M$ appears in a spinless configuration ($M\ensuremath{\sim}70$ MeV), and also in a relativistically spinning configuration (${M}_{s}\ensuremath{\sim}110$ MeV) as the nucleon quark $S\ensuremath{\equiv}3{M}_{s}\ensuremath{\sim}330$ MeV. The mass ratio $\frac{{M}_{s}}{M}\ensuremath{\sim}\frac{3}{2}$ is a calculated quantity. The model can be formulated with a total of ten quark-state parameters: the masses ${M}^{0}=70.0$ MeV, ${M}^{\ifmmode\pm\else\textpm\fi{}}=74.6$ MeV, ${S}^{\ifmmode\pm\else\textpm\fi{}}=330.6$ MeV, and ${S}^{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}}=336.9$ MeV; the hadronic binding energies $M\overline{M}=\ensuremath{-}5.0$ MeV, $M{\overline{M}}_{s}=\ensuremath{-}5.0$ MeV, and ${M}_{s}{\overline{M}}_{s}=\ensuremath{-}9.1$ MeV; a magnetic binding energy ${S}^{\ifmmode\pm\else\textpm\fi{}}{S}^{\ifmmode\pm\else\textpm\fi{}}=\ifmmode\pm\else\textpm\fi{}1.7$ MeV; a magnetic moment ${\ensuremath{\mu}}_{{S}^{\ifmmode\pm\else\textpm\fi{}}}=\ifmmode\pm\else\textpm\fi{}9.3$ nuclear magnetons (${\ensuremath{\mu}}_{N}$); and a radius ${R}_{M}\ensuremath{\simeq}0.6$ fermi. The spin angular momentum $J=\frac{1}{2}\ensuremath{\hbar}$ of the spinor $S$ is a calculated quantity, and the model also includes small calculated Coulomb corrections arising from multiple internal charges. With this formulation, the masses of all of the fundamental narrow-width hadron resonances---${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${\ensuremath{\pi}}^{0}$, ${K}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{0}$, $\ensuremath{\eta}$, $M$, ${\ensuremath{\eta}}^{\ensuremath{'}}$, ${\ensuremath{\delta}}^{0}$, $p$, $n$, $\overline{p}n$, $\ensuremath{\Lambda}$, ${\ensuremath{\Sigma}}^{+}$, ${\ensuremath{\Sigma}}^{0}$, ${\ensuremath{\Sigma}}^{\ensuremath{-}}$, ${\ensuremath{\Xi}}^{0}$, ${\ensuremath{\Xi}}^{\ensuremath{-}}$, and ${\ensuremath{\Omega}}^{\ensuremath{-}}$---are calculated to an average absolute accuracy of \ifmmode\pm\else\textpm\fi{} 0.1%, or \ifmmode\pm\else\textpm\fi{} 1 MeV, and spins, charge splittings, magnetic moments, and strangeness quantum numbers are reproduced. These calculated mass values are accurate enough to pinpoint the $M$ meson as the fundamental ground-state member of the $M(953)$, ${\ensuremath{\eta}}^{\ensuremath{'}}(958)$, ${\ensuremath{\delta}}^{0}(963)$ multiplet, a result that is experimentally confirmed by both the production modes and the decay modes for these mesons.