$\bar{D}\Sigma^*_c$ and $\bar{D}^*\Sigma_c$ 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 $\bar{D}\Sigma_c^*(2520)$ and $\bar{D}^*\Sigma_c(2455)$ 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 $\bar{D}^*\Sigma_c(2455)$ interaction with spin parities $3/2^-$ and $5/2^+$, respectively. The peak for $5/2^+$ state has a comparable hight as that of $3/2^-$ state in the $J/\psi p$ invariant mass spectrum. Another bound state with spin-parity $J^P=3/2^-$ is produced from the $\bar{D}\Sigma^*_c(2520)$ interaction. Such results suggest that the narrower LHCb pentaquark $P_c(4450)$ can be well interpreted as a $5/2^+$ $\bar{D}^*\Sigma_c(2455)$ molecular state while the $P_c(4380)$ is a $3/2^-$ $\bar{D}^*\Sigma_c(2455)$ molecular state mixed with other secondary origins.