Pentaquark baryons in the SU(3) quark model

We study the SU(3) group structure of pentaquark baryons which are made of four quarks and one antiquark. The pentaquark baryons form $\mathbf{1}$, $\mathbf{8}$, $\mathbf{10}$, $\overline{\mathbf{10}}$, $\mathbf{27}$, and $\mathbf{35}$ multiplets in the SU(3) quark model. First, the flavor wave functions of all the pentaquark baryons are constructed in the SU(3) quark model and then the flavor SU(3) symmetry relations for the interactions of the pentaquarks with three-quark baryons and pentaquark baryons are obtained. Constructing the general interactions in SU(3) could be important for understanding the pentaquark baryon properties from reaction mechanisms. We also discuss possible pentaquarks in $\mathbf{27}$-plet and $\mathbf{35}$-plet and their decay channels that can be used to identify them in future experiments. The mass sum rules for the pentaquark baryons are also presented.

Figure 1

Product of two quarks, $\mathbf{3}\otimes \mathbf{3}=\mathbf{6}\oplus \overline{\mathbf{3}}$.

Figure 2

Products of two diquarks. (a) $\mathbf{6}\otimes \mathbf{6}={\mathbf{15}}_1\oplus {\mathbf{15}}_2\oplus \overline{\mathbf{6}}$, (b) $\mathbf{6}\otimes \overline{\mathbf{3}}={\mathbf{15}}_2\oplus \mathbf{3}$,and (c) $\overline{\mathbf{3}}\otimes \overline{\mathbf{3}}=\overline{\mathbf{6}}\oplus \mathbf{3}$.

Figure 3

Products of two diquarks and one antiquark. (a) ${\mathbf{15}}_1\otimes \overline{\mathbf{3}}=\mathbf{35}\oplus \mathbf{10}$,(b) ${\mathbf{15}}_2\otimes \overline{\mathbf{3}}=\mathbf{27}\oplus \mathbf{10}\oplus \mathbf{8}$, (c) $\overline{\mathbf{6}}\otimes \overline{\mathbf{3}}=\overline{\mathbf{10}}\oplus \mathbf{8}$, and (d) $\mathbf{3}\otimes \overline{\mathbf{3}}=\mathbf{8}\oplus \mathbf{1}$.

Figure 4

Weight diagram for the pentaquark octet.

Figure 5

Weight diagram for the pentaquark decuplet.

Figure 6

Weight diagram for the pentaquark antidecuplet.

Figure 7

Weight diagram for the pentaquark $\mathbf{27}$-plet.

Figure 8

Weight diagram for the pentaquark $\mathbf{35}$-plet.