Meson Masses and Decays

Abstract

We consider here the masses, decay rates, and decay spectra of the octet of $0^{-}$ mesons, the nonet of $1^{-}$ mesons, the $X\left(960\right)\mathrm{}$ resonance, and a proposed ${\eta }^{*}\mathrm{}\left(1620\right)\mathrm{}$ resonance having the quantum numbers of $\eta \mathrm{}\left(550\right)\mathrm{}$. We use spin-unitary-spin symmetry and nonet symmetry, so that the mesons fall into 36 states, combining an $\mathrm{SU}\left(6\right)\mathrm{}1$, with an $\mathrm{SU}\left(6\right)\mathrm{}35$. Further, we fix the strength of the couplings of the $\mathrm{SU}\left(3\right)\mathrm{}$ octets in the 36 with respect to the $\mathrm{SU}\left(3\right)\mathrm{}$ singlets by assuming that the form of the coupling remains unchanged when we include the singlet states. We are then able—after making a particular choice of Hamiltonion—to predict the masses $M_{{\eta }^{*}},M_{{\rho }^{\pm }},M_{{\rho }^0},M_{K^{*\pm }},M_{K^{*0\mathrm{}}}$ and the decay rates ${\Gamma }_{\omega \to {\pi }^{+}{\pi }^{-}}$, ${\Gamma }_{\phi \to {\pi }^{+}{\pi }^{-}}$, ${\Gamma }_{\phi \to {\pi }^{+}{\pi }^{-}{\pi }^0}$, using as input the masses of the octet of $0^{-}$ mesons and $M_{\phi },M_{\omega }$. These predictions are in reasonable agreement with presently existing experimental data. We further discuss related meson decays using the above scheme to eliminate the arbitrariness in the relative coupling strength of the singlet states. Specifically we consider $V\to P+P^{\prime }$, $V\to 3P$, $V\to P+\gamma$, $V\to P+P^{\prime }+\gamma$ [discussing $C$ noninvariance and $S$-wave pion-pion resonances and their effect in $(\omega ,\phi )\to {\pi }^{+}{\pi }^{-}\gamma$, $V\to l^{+}+l^{-}$, $P\to 2\gamma$, $P\to P^{\prime }+P^{\prime \prime }+\gamma$, and $P\to l^{+}+l^{-}+\gamma$. We use the model of Gell-Mann, Sharp, and Wagner and give invariant-mass spectra for the three-body decays.