Diquarks in nonaquark states

Abstract

We study the nonaquark states ${S}^{0}(3115)$ and ${S}^{+}(3140)$ which are reported by [T. Suzuki (KEK-PS), Phys. Lett. B 597, 236 (2004)M. Iwasaki et al., nucl-ex/0310018] by means of the quark model with diquark correlation. The nonaquark states form $\mathbf{1},\mathbf{8},\mathbf{10},\overline{\mathbf{10}},\mathbf{27},\overline{\mathbf{35}}$ SU(3) multiplets. The flavor wave functions of all the nonaquark states are constructed through the standard tensor technique. The mass spectrum is studied by using the Gell-Mann-Okubo mass formula. Some nonaquark mass sum rules are obtained. We further investigate the decay of ${S}^{0}(3115)$ and ${S}^{+}(3140)$ under the assumption of the ``fall-apart'' mechanism. It has been found that the main decay mode is $\ensuremath{\Sigma}NN$ rather than $\ensuremath{\Lambda}NN$ which is consistent with experiment. Also we have uniquely determined the flavor wave function of ${S}^{0}(3115)$ which belongs to the $\mathbf{27}$-plet with the quantum number $Y=2,I=1,{I}_{z}=\ensuremath{-}1$. Whereas the exotic states ${S}^{+}(3140)$ can belong to either the $\mathbf{27}$-plet or the $\overline{\mathbf{35}}$-plet. In the exact $\mathrm{SU}(3{)}^{\mathrm{flavor}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}^{\mathrm{color}}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2{)}^{\mathrm{spin}}$ limit, both ${S}^{0}(3115)$ and ${S}^{+}(3140)$ belong to the $\mathbf{27}$-plet with negative parity. We predict that its flavor structure can be determined by measuring the branch fractions of its decay channels. The experiments to check this prediction are as expected.