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Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory

We calculate the effective potentials of the $Ξ_c\bar{D}^{(\ast)}$, $Ξ_c^\prime\bar{D}^{(\ast)}$ and $Ξ_c^\ast\bar{D}^{(\ast)}$ systems with the chiral effective field theory up to the next-to-leading order. We simultaneously consider the short-, intermediate- and long-range interactions. With the newly observed $P_c$ spectra as inputs, we construct the quark-level contact Lagrangians to relate the low energy constants to those of $Σ_c\bar{D}^{(\ast)}$ with the help of quark model. Our calculation indicates there are seven bound states in the $I=0$ strange hidden charm $[Ξ_c^\prime\bar{D}^{(\ast)}]_J~(J=\frac{1}{2},\frac{3}{2})$ and $[Ξ_c^\ast\bar{D}^{(\ast)}]_J~(J=\frac{1}{2},\frac{3}{2},\frac{5}{2})$ systems. Our analyses also disfavor the $Λ_c\bar{D}^{(\ast)}$ bound states. However, we obtain three new hadronic molecules in the isoscalar $[Ξ_c\bar{D}^{(\ast)}]_J~(J=\frac{1}{2},\frac{3}{2})$ systems. The masses of $[Ξ_c\bar{D}]_{1/2}$, $[Ξ_c\bar{D}^{\ast}]_{1/2}$ and $[Ξ_c\bar{D}^{\ast}]_{3/2}$ are predicted to be $4319.4^{+2.8}_{-3.0}$ MeV, $4456.9^{+3.2}_{-3.3}$ MeV and $4463.0^{+2.8}_{-3.0}$ MeV, respectively. We also notice the one-eta-exchange influence is rather feeble. Binding solutions in the $I=1$ channels are nonexistent. We hope the future analyses at LHCb can seek for these new $P_{cs}$s in the $JψΛ$ final states, especially near the thresholds of $Ξ_c\bar{D}^{(\ast)}$.