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

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Abstract

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

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