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Molecular states from $Σ^{(*)}_c\bar{D}^{(*)}-Λ_c\bar{D}^{(*)}$ interaction

In this work, we systemically investigate the molecular states from the $Σ^{(*)}_c\bar{D}^{(*)}-Λ_c\bar{D}^{(*)}$ interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe-Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) $Σ_c\bar{D}$ interaction with spin parity $J^P=1/2^-$ and $Σ_c\bar{D}^*$ interaction with $1/2^-$ and $ 3/2^-$. Their masses and widths are consistent with the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ observed at LHCb. The states, $Σ_c^*\bar{D}^*(1/2^-)$, $Σ_c^*\bar{D}^*(3/2^-)$ and $Σ^*_c\bar{D}(3/2^-)$, are also produced with the same parameters. The isodoublet $Σ_c^*\bar{D}^*$ interaction with $5/2^-$, as well as the isoquartet (I=3/2) $Σ_c\bar{D}^*$ interactions with $1/2^-$ and $3/2^-$, $Σ_c^*\bar{D}^*$ interaction with $3/2^-$ and $5/2^-$, are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The $Λ\bar{D}^*$ channel is dominant in the decays of the states, $Σ_c\bar{D}^*(1/2^-)$, $Σ_c\bar{D}^*(3/2^-)$, $Σ_c^*\bar{D}(3/2^-)$, and $Σ_c\bar{D}(1/2^-)$. The $Σ^*_c\bar{D}^*(1/2^-)$ state has large coupling to $Σ_c\bar{D}$ channel while the $Σ_c\bar{D}^*$, $Σ^*_c\bar{D}$ and $Λ_c\bar{D}^*$ channels provide similar contributions to the width of the $Σ^*_c\bar{D}^*(3/2^-)$ state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.