$\bar{D}{\mathrm{\Sigma }}_c^{\ast }$ and ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c$ interactions and LHCb pentaquarks

Recently, LHCb collaboration reported the observation of two hidden-charmed resonances $P_c(4380)$ and $P_c(4450)$ consistent with hidden-charmed pentaquarks. We perform a dynamical investigation about the $\bar{D}{\mathrm{\Sigma }}_c^{\ast }(2520)$ and ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c(2455)$ interactions which are described by the meson exchanges in a quasipotential Bethe-Salpeter equation approach. Two poles around $4450$ and $4390$ MeV are produced from the ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c(2455)$ interaction with spin parities $3\mathrm{/}{2}^{-}$ and $5\mathrm{/}{2}^{+}$, respectively. The peak for $5\mathrm{/}{2}^{+}$ state has a comparable hight as that of $3\mathrm{/}{2}^{-}$ state in the $J\mathrm{/}\psi p$ invariant mass spectrum. Another bound state with spin-parity $J^P=3\mathrm{/}{2}^{-}$ is produced from the $\bar{D}{\mathrm{\Sigma }}_c^{\ast }(2520)$ interaction. Such results suggest that the narrower LHCb pentaquark $P_c(4450)$ can be well interpreted as a $5\mathrm{/}{2}^{+}$ ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c(2455)$ molecular state while the $P_c(4380)$ is a $3\mathrm{/}{2}^{-}$ ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c(2455)$ molecular state mixed with other secondary origins.