Strong decay mode $J/\psi p$ of hidden charm pentaquark states $P_c^{+}(4380)$ and $P_c^{+}(4450)$ in ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ molecular scenario

We study the strong decay channels $P_c^{+}(4380)\to J/\psi p$ and $P_c^{+}(4450)\to J/\psi p$ under a ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ molecular state ansatz. With various spin-parity assignments, the partial decay widths of the $J/\psi p$ final state are calculated. Our results show that all the $P$ wave ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ assignments are excluded, while $S$ wave ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ pictures for $P_c(4380)$ and $P_c(4450)$ are both allowed by present experimental data. The $J^P=3/2^{-}$ ${\mathrm{\Sigma }}_c^{*}\overline{D}$ and ${\mathrm{\Sigma }}_c^{*}{\overline{D}}^{*}$ molecules are also discussed in the heavy quark limit, and we find that the ${\mathrm{\Sigma }}_c^{*}\overline{D}$ system for $P_c(4380)$ is possible. More experimental information on spin parities and partial decay widths and theoretical investigations on other decay modes are needed to clarify the nature of the two $P_c$ states.

Figure 1

The mass operator of $P_c^{+}$ states.

Figure 2

Feynman diagrams for the $P_c^{+}\to J/\psi p$ decay process.

Figure 3

The coupling constants of $P_c$ states with different $J^P$ assignments depending on the parameter $\mathrm{\Lambda }$. The red solid line stands for $P=+$, and the green dashed line corresponds to $P=-$ cases.

Figure 4

The partial decay widths of the $P_c^{+}(4380)\to J/\psi p$ with different $J^P$ assignments depending on the parameter $\mathrm{\Lambda }$. The red dashed, green dotted, pink short dotted, and blue dotted-dashed lines stand for the $J^P=3/2^{+},3/2^{-},5/2^{+}$ and $5/2^{-}$ cases, respectively. The black solid line and blue error band correspond to the total width observed by experiment.

Figure 5

The same as Fig. 4, but for the $P_c^{+}(4450)\to J/\psi p$. The partial decay width of the $J^P=3/2^{+}$ case is much larger than the experimental data and neglected here.

Figure 6

The individual contributions of the $D^{*}$, $D$, and ${\mathrm{\Sigma }}_c$ exchanges for the $P_c^{+}(4380)\to J/\psi p$ with different $J^P$ assignments. The red solid, green dotted, blue dotted-dashed, and pink short dotted lines stand for the total, $D^{*}$, $D$, and ${\mathrm{\Sigma }}_c$ contributions, respectively.