Diquark in Nona-quark States

Abstract

We study the nonaquark states $S^0(3115)$ and $S^+(3140)$ which are reported by KEK-PS (Phys.Lett. B597 (2004) 236; nucl-ex/0310018) by means of the quark model with diquark correlation. The nonaquark states form $\bf{1},\bf{8},\bf{10},\bar{\bf{10}},\bf{27},\bar{\bf{35}}$ 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 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 "fall-apart" mechanism. It has been found that the main decay mode is $ΣNN$ rather than $ΛNN$ which is consistent with experiment. Also we have uniquely determine the flavor wave function of $S^0(3115)$ which belong to $\bf{27}$-plet with the quantum number $Y=2,I=1,I_z=-1$. Whereas the exotic states $S^+(3140)$ can belong to either $\bf{27}$-plet or $\bar{\bf{35}}$-plet. In the exact $SU(3)^{flavor}\times SU(3)^{color}\times SU(2)^{spin}$ limit, both $S^0(3115)$ and $S^+(3140)$ belong to ${\bf 27}$-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 expected.