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In the framework of the color-magnetic interaction, we have systematicallystudied the mass splittings of the possible hidden-charm pentaquarks$qqqc\bar{c}$ ($q=u,d,s$) where the three light quarks are in a color-octetstate. We find that i) the LHCb $P_c$ states fall in the mass region of thestudied system; ii) most pentaquarks should be broad states since their$S$-wave open-charm decays are allowed while the lowest state is the$J^P=\frac12^-$ $\Lambda$-like pentaquark with probably the suppressed$\eta_c\Lambda$ decay mode only; and iii) the $J^P=\frac52^-$ states do notdecay through $S$-wave and their widths are not so broad. The masses and widthsof the two LHCb $P_c$ baryons are compatible with such pentaquark states. Wealso explore the hidden-bottom and $B_c$-like partners of the hidden-charmstates and find the possible existence of the pentaquarks which are lower thanthe relevant hadronic molecules.

Hidden-charm pentaquarks and their hidden-bottom and $B_c$-like partner states