$P_{cs}(4459)$ and other possible molecular states from $\hat{I}{ž}_c^{(\ast )}{\bar{D}}^{(\ast )}$ and $\hat{I}{ž}_c^{\prime }{\bar{D}}^{(\ast )}$ interactions

Abstract

Recently, the LHCb Collaboration reported a new structure $P_{cs}(4459)$ with a mass of 19 MeV below the $\hat{I}{ž}_c{\bar{D}}^{\ast }$ threshold. It may be a candidate of molecular state from the $\hat{I}{ž}_c{\bar{D}}^{\ast }$ interaction. In the current work, we perform a coupled-channel study of the $\hat{I}{ž}_c^{\ast }{\bar{D}}^{\ast }$, $\hat{I}{ž}_c^{\prime }{\bar{D}}^{\ast }$, $\hat{I}{ž}_c^{\ast }\bar{D}$, $\hat{I}{ž}_c{\bar{D}}^{\ast }$, $\hat{I}{ž}_c^{\prime }\bar{D}$, and $\hat{I}{ž}_c\bar{D}$ interactions in the quasipotential Bethe-Salpeter equation approach. With the help of the heavy quark chiral effective Lagrangian, the potential is constructed by light meson exchanges. Two $\hat{I}{ž}_c{\bar{D}}^{\ast }$ molecular states are produced with spin parities $J^P=1/2^{-}$ and $3/2^{-}$. The lower state with $3/2^{-}$ can be related to the observed $P_{cs}(4450)$ while two-peak structure cannot be excluded. Within the same model, other strange hidden-charm pentaquarks are also predicted. Two states with spin parities $1/2^{-}$ and $3/2^{-}$ are predicted near the $\hat{I}{ž}_c^{\prime }\bar{D}$, $\hat{I}{ž}_c\bar{D}$, and $\hat{I}{ž}_c^{\ast }\bar{D}$ thresholds, respectively. As two states near $\hat{I}{ž}_c{\bar{D}}^{\ast }$ threshold, two states are produced with $1/2^{-}$ and $3/2^{-}$ near the $\hat{I}{ž}_c^{\prime }{\bar{D}}^{\ast }$ threshold. The couplings of the molecular states to the considered channels are also discussed. The experimental research of those states are helpful to understand the origin and internal structure of the $P_{cs}$ and $P_c$ states.

7 pages, 2 figures