Molecular states from

In this work, we systemically investigate the molecular states from the $$\varSigma ^{(*)}_c{\bar{D}}^{(*)}-\varLambda _c{\bar{D}}^{(*)}$$ 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) $$\varSigma _c{\bar{D}}$$ interaction with spin parity $$J^P=1/2^-$$ and $$\varSigma _c{\bar{D}}^*$$ 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, $$\varSigma _c^*{\bar{D}}^*(1/2^-)$$, $$\varSigma _c^*{\bar{D}}^*(3/2^-)$$ and $$\varSigma ^*_c{\bar{D}}(3/2^-)$$, are also produced with the same parameters. The isodoublet $$\varSigma _c^*{\bar{D}}^*$$ interaction with $$5/2^-$$, as well as the isoquartet (I=3/2) $$\varSigma _c{\bar{D}}^*$$ interactions with $$1/2^-$$ and $$3/2^-$$, $$\varSigma _c^*{\bar{D}}^*$$ 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 $$\varLambda {\bar{D}}^*$$ channel is dominant in the decays of the states, $$\varSigma _c{\bar{D}}^*(1/2^-)$$, $$\varSigma _c{\bar{D}}^*(3/2^-)$$, $$\varSigma _c^*{\bar{D}}(3/2^-)$$, and $$\varSigma _c{\bar{D}}(1/2^-)$$. The $$\varSigma ^*_c{\bar{D}}^*(1/2^-)$$ state has large coupling to $$\varSigma _c{\bar{D}}$$ channel while the $$\varSigma _c{\bar{D}}^*$$, $$\varSigma ^*_c{\bar{D}}$$ and $$\varLambda _c{\bar{D}}^*$$ channels provide similar contributions to the width of the $$\varSigma ^*_c{\bar{D}}^*(3/2^-)$$ 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