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Recently, a new hidden-charm pentaquark state $$P_{cs}(4459)$$ P cs ( 4459 ) was reported by the LHCb Collaboration. Stimulated by the fact that all hidden-charm pentaquark states in $$S=0$$ S = 0 systems were successfully studied by the chiral quark model, we extended this study to the $$S=-1$$ S = - 1 systems. All possible states with quantum numbers $$IJ^P=0(\frac{1}{2})^-$$ I J P = 0 ( 1 2 ) - , $$0(\frac{3}{2})^-$$ 0 ( 3 2 ) - , $$0(\frac{5}{2})^-$$ 0 ( 5 2 ) - , $$1(\frac{1}{2})^-$$ 1 ( 1 2 ) - , $$1(\frac{3}{2})^-$$ 1 ( 3 2 ) - and $$1(\frac{5}{2})^-$$ 1 ( 5 2 ) - have been investigated. The calculation results shows that the newly observed state $$P_{cs}(4459)$$ P cs ( 4459 ) can be explained as $$\Xi _c \bar{D}^*$$ Ξ c D ¯ ∗ molecular state and the quantum numbers are $$0(\frac{1}{2})^-$$ 0 ( 1 2 ) - . In addition, we also find other molecular states $$\Xi _c \bar{D}$$ Ξ c D ¯ , $$\Xi _c^* \bar{D}$$ Ξ c ∗ D ¯ and $$\Xi _c' \bar{D}^*$$ Ξ c ′ D ¯ ∗ . It is worth mentioning that $$\Xi _c \bar{D}^*$$ Ξ c D ¯ ∗ can form a two-peak structure from states in system $$0(\frac{1}{2})^-$$ 0 ( 1 2 ) - and $$0(\frac{3}{2})^-$$ 0 ( 3 2 ) - . The decay width of all molecular states is given with the help of real scaling method. These hidden-charm pentaquark states is expected to be further verified in future experiments.

With the discovery of some hidden-charm pentaquark resonances by the LHCb Collaboration, investigations of pentaquark states containing heavy quarks have aroused the interest of theorists. We study herein $$qqq{\bar{q}}Q$$ q q q q ¯ Q ($$q = u$$ q = u or d, $$Q=c$$ Q = c or b) pentaquark system, in the framework of the chiral quark model. In consequence, some charmed and bottomed pentaquarks are considered to exist by five-body dynamical calculations. In the charm sector, $$\Sigma _c\pi (IJ^P=0\frac{1}{2}^-)$$ Σ c π ( I J P = 0 1 2 - ) and $$\Sigma _c^*\pi (IJ^P=0\frac{3}{2}^-)$$ Σ c ∗ π ( I J P = 0 3 2 - ) are possible candidates of $$\Lambda _c(2595)$$ Λ c ( 2595 ) and $$\Lambda _c(2625)$$ Λ c ( 2625 ) , respectively. Besides, two high-spin states, $$\Sigma _c^*\rho (IJ^P=0\frac{5}{2}^-)$$ Σ c ∗ ρ ( I J P = 0 5 2 - ) and $$\Delta D^*(IJ^P=1\frac{5}{2}^-)$$ Δ D ∗ ( I J P = 1 5 2 - ) , are also found in the energy region of $$3.2 \sim 3.3$$ 3.2 ∼ 3.3 GeV. In the bottom sector, $$\Sigma _b\pi (IJ^P=0\frac{1}{2}^-)$$ Σ b π ( I J P = 0 1 2 - ) , $$\Sigma _b^*\pi (IJ^P=0\frac{3}{2}^-)$$ Σ b ∗ π ( I J P = 0 3 2 - ) could be candidates of $$\Lambda _b(5912)$$ Λ b ( 5912 ) and $$\Lambda _b(5920)$$ Λ b ( 5920 ) , respectively. And $$\Sigma _b^*\rho (IJ^P=0\frac{5}{2}^-)$$ Σ b ∗ ρ ( I J P = 0 5 2 - ) and $$\Delta B^*(IJ^P=1\frac{5}{2}^-)$$ Δ B ∗ ( I J P = 1 5 2 - ) are found in the energy region of $$6.5 \sim 6.6$$ 6.5 ∼ 6.6 GeV. $$\Sigma _c^{(*)}\pi $$ Σ c ( ∗ ) π and $$\Sigma _b^{(*)}\pi $$ Σ b ( ∗ ) π are expected as compact states, while $$\Sigma _c^*\rho $$ Σ c ∗ ρ , $$\Sigma _b^*\rho $$ Σ b ∗ ρ , $$\Delta D^*$$ Δ D ∗ and $$\Delta B^*$$ Δ B ∗ are expected as molecular states.

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Recently, three new states of $$\varXi _c^0$$ Ξ c 0 were observed in the invariant mass spectrum of $$\varLambda ^+_cK^-$$ Λ c + K - by LHCb collaboration. In this work, we use a chiral quark model to investigate these three exited states with the help of Gaussian expansion method both in three-quark structure and in five-quark structure with all possible quantum numbers $$IJ^P=\frac{1}{2}(\frac{1}{2})^-$$ I J P = 1 2 ( 1 2 ) - , $$\frac{1}{2}(\frac{3}{2})^-$$ 1 2 ( 3 2 ) - , $$\frac{1}{2}(\frac{5}{2})^-$$ 1 2 ( 5 2 ) - , $$\frac{3}{2}(\frac{1}{2})^-$$ 3 2 ( 1 2 ) - , $$\frac{3}{2}(\frac{3}{2})^-$$ 3 2 ( 3 2 ) - and $$\frac{3}{2}(\frac{5}{2})^-$$ 3 2 ( 5 2 ) - . The calculations shows that the masses of 2S and 1D states of $$\varXi _c$$ Ξ c are comparable to experimental results; In addition, the resonance states of five-quark configuration are possible candidates of these new states with negative parity by using the real scaling method and their decay width is also given.