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

Abstract

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

Comments: 9 pages, 2 figures, and 4 tables