Analysis of $P_c^{+}(4380)$ and $P_c^{+}(4450)$ as pentaquark states in the molecular picture with QCD sum rules

To better understand the nature and internal structure of the exotic states discovered by many collaborations, more information on their electromagnetic properties and their strong and weak interactions with other hadrons is needed. The residue or current coupling constant of these states together with their mass are the main inputs in determinations of such properties. We perform QCD sum rules analyses on the hidden-charm pentaquark states with spin parities $J^P={\frac{3}{2}}^{\pm }$ and $J^P={\frac{5}{2}}^{\pm }$ to calculate their residue and mass. In the calculations, we adopt a molecular picture for $J^P={\frac{3}{2}}^{\pm }$ states and a mixed current in a molecular form for $J^P={\frac{5}{2}}^{\pm }$. Our analyses show that the $P_c^{+}(4380)$ and $P_c^{+}(4450)$, observed by the LHCb Collaboration, can be considered as hidden-charm pentaquark states with $J^P={\frac{3}{2}}^{-}$ and $J^P={\frac{5}{2}}^{+}$, respectively.

Figure 1

Left: The mass of the pentaquark with $J^P={\frac{5}{2}}^{+}$ as a function of the Borel parameter $M^2$ at different fixed values of the continuum threshold. Right: The residue of the pentaquark with $J^P={\frac{5}{2}}^{+}$ as a function of the Borel parameter $M^2$ at different fixed values of the continuum threshold.

Figure 2

Left: The mass of the pentaquark with $J^P={\frac{5}{2}}^{+}$ as a function of $s_0$ at different fixed values of the Borel parameter. Right: The residue of the pentaquark with $J^P={\frac{5}{2}}^{+}$ as a function of $s_0$ at different fixed values of the Borel parameter.