We calculate the effective potentials of the ${\mathrm{\Xi }}_c{\overline{D}}^{(*)}$, ${\mathrm{\Xi }}_c^{\prime }{\overline{D}}^{(*)}$, and ${\mathrm{\Xi }}_c^{*}{\overline{D}}^{(*)}$ system s 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 ${\mathrm{\Sigma }}_c{\overline{D}}^{(*)}$ with the help of the quark model. Our calculation indicates there are seven bound states in the $I=0$ strange hidden charm $[{\mathrm{\Xi }}_c^{\prime }{\overline{D}}^{(*)}{]}_J(J=\frac{1}{2},\frac{3}{2})$ and $[{\mathrm{\Xi }}_c^{*}{\overline{D}}^{(*)}{]}_J(J=\frac{1}{2},\frac{3}{2},\frac{5}{2})$ systems. Our analyses also disfavor the ${\mathrm{\Lambda }}_c{\overline{D}}^{(*)}$ bound states. However, we obtain three new hadronic molecules in the isoscalar $[{\mathrm{\Xi }}_c{\overline{D}}^{(*)}{]}_J(J=\frac{1}{2},\frac{3}{2})$ systems. The masses of $[{\mathrm{\Xi }}_c\overline{D}{]}_{1/2}$, $[{\mathrm{\Xi }}_c{\overline{D}}^{*}{]}_{1/2}$, and $[{\mathrm{\Xi }}_c{\overline{D}}^{*}{]}_{3/2}$ are predicted to be ${4319.4}_{-3.0}^{+2.8}\mathrm{MeV}$, ${4456.9}_{-3.3}^{+3.2}\mathrm{MeV}$, and ${4463.0}_{-3.0}^{+2.8}\mathrm{MeV}$, 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 $P_{cs}\mathrm{s}$ in the $J\psi \mathrm{\Lambda }$ final states, especially near the thresholds of ${\mathrm{\Xi }}_c{\overline{D}}^{(*)}$.

• Received 31 December 2019
• Accepted 3 February 2020

DOI:https://doi.org/10.1103/PhysRevD.101.034018

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Published by the American Physical Society