Vector-meson decays in the SLAC lattice quantum-chromodynamic theory

The large-distance-dominated hadronic decays of the $K^{*}$, $\phi$, and $\omega$ mesons of the lowest-lying vector-meson nonet of ordinary flavor SU(3) symmetry are discussed from the point of view of the SLAC lattice Hamiltonian QCD theory. The agreement between our theoretical results and observation is reasonable. This agreement we take as further evidence for the applicability of the two key ingredients in our calculational procedure to large-distance hadron dynamics. Here, we have reference to (a) the vacuum-insertion technique of Lee, Primack, and Treiman for the evaluation of light-hadron matrix elements of effective low-energy interacting densities and (b) the identification of the SLAC lattice currents with the physical hadron currents to leading order in the SLAC order-$\frac{1}{g^2}$ effective Hamiltonian for the fluxless light-hadron sector—in the spirit of Gell-Mann's work in current algebra. Indeed, when the results of the present paper are combined with our result for the decay $\rho \to \pi \pi$ in the same theoretical framework, we may say that the SLAC lattice QCD theory, taken together with these two techniques, represents a viable scheme for understanding the large-distance aspects of the hadronic decays of the entire vector-meson nonet of the ordinary SU(3) flavor symmetry.