Molecular nature of $P_{cs} (4459)$ and its heavy quark spin partners


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Inspired by the observation of the $P_{cs} (4459)$ state by LHCb recently, we reexamine the results of the interaction of the $J/psi Lambda$ channel with its coupled channels, exploiting the coupled channel unitary approach combined with heavy quark spin and local hidden gauge symmetries. By tuning the only free parameter, we find a pole of $(4459.07+i6.89)$ MeV below the $bar D^* Xi_c$ threshold, which was consistent well with the mass and width of the $P_{cs} (4459)$ state. Thus, we assume the $P_{cs} (4459)$ state to be a $bar D^* Xi_c$ bound state with the uncertainties on its degeneracy with $J^P = frac{1}{2}^-$ and $J^P = frac{3}{2}^-$. For the degeneracy, it would have two-poles structure, like $P_c (4450)$ before. There is another pole in the $J^P = frac{1}{2}^-$ sector, $(4310.53+i8.23)$ MeV, corresponding to a deep bound state of $bar D Xi_c$. Furthermore, the previously predicted loose bound states of $bar D Xi_c$, $bar D^* Xi_c$, $bar D^* Xi^*_c$ with $J=1/2,~I=0$ and $bar D^* Xi_c$, $bar D Xi^*_c$, $bar D^* Xi_c^*$ with $J=3/2,~I=0$ may exist as either bound states or unbound virtual states. We hope that future experiments can search for the $bar D^{(*)} Xi_c$ molecular states in their dominant decay channels of $bar D^{(*)}_s Lambda_c$, also in the $J/psi Lambda$ and $eta_c Lambda$ channels to reveal their different nature.

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