Narrow $J^{\pi }=1/2^{+},3/2^{+}$, and $3/2^{-}$ states of ${\Theta }^{+}$ in a quark model with antisymmetrized molecular dynamics

The exotic baryon ${\Theta }^{+}(\mathit{uudd}\overline{s})$ is studied with microscopic calculations in a quark model by using a method of antisymmetrized molecular dynamics. We predict that three narrow states, $J^{\pi }=1/2^{+}(I=0),J^{\pi }=3/2^{+}(I=0)$, and $J^{\pi }=3/2^{-}(I=1)$ nearly degenerate with the lowest $1/2^{-}$ state in the $\mathit{uudd}\overline{s}$ system. We discuss $\mathrm{KN}$ decay widths and estimate them to be $\Gamma <7$ for the $J^{\pi }=\{1/2^{+},3/2^{+}\}$, and $\Gamma <1\hspace{1em}\mathrm{MeV}$ for the $J^{\pi }=3/2^{-}$ state. In contrast to these narrow states, the $1/2^{-}$ states should be much broader. We assign the observed ${\Theta }^{+}$ as the $J^{\pi }=\{1/2^{+},3/2^{+}\}$.

Figure 1

Flux-tube configurations for confined states of $q\overline{q}$ (a), $q^3$ (b), $q^4\overline{q}$ (c) and the disconnected flux tube of $q^4\overline{q}$ (d). Figures (e) and (f) represent the flux tubes in the color configurations, $[\mathit{ud}][\mathit{ud}]\overline{s}$ and $[\mathit{uu}][\mathit{dd}]\overline{s}$, respectively.

Figure 2

Flux-tube topologies for the $q\overline{q}$ (a), $q^3$ (b), $[q_1{q}_2][q_3{q}_4]\overline{q_1}$ (c) and disconnected flux tubes (d) for the $(\mathit{qqq}){}_1(q\overline{q}){}_1$. The flux-tube topologies are described by the bonds with the lengths $R_k$ and the junctions $j_k$.

Figure 3

The ratio $L_{\mathrm{app}}/L_f$ for the approximated tube length $L_{\mathrm{app}}$ and the exact tube length $L_f$ in a $q^3$ system and a $[\mathit{qq}][\mathit{qq}]\overline{q}$ system. The quark positions $r_i$ are randomly chosen in Gaussian deviates with the probability $\rho =\exp (-r_i^2/b^2)$, and $(L_f,L_{\mathrm{app}}/L_f)$ values for 1000 samplings are plotted.

Figure 4

The q and $\overline{q}$ density distribution in the $J^{\pi }=1/2^{+},3/2^{+}(S=1/2,L=1)$ states of the $\mathit{uudd}\overline{s}$ system. The u density (a), $\overline{s}$ density (b), and total quark-antiquark density (c) of the intrinsic state before parity projection are shown. The schematic figure of the corresponding flux-tube configuration is illustrated in (d). Open squares in (a) and (b) indicate the positions of Gaussian centers $\mathrm{Re}[\sqrt{2}b{Z}_i]$ for the i-th single-particle wave functions.