The $P_{cs}(4459)$ pentaquark from a combined effective field theory and phenomenological perspective
Résumé
The observation of the $P_{cs}(4459)$ by the LHCb collaboration adds a new member to the set of known hidden-charm pentaquarks, which includes the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. The $P_{cs}(4459)$ is expected to have the light-quark content of a $\Lambda $ baryon ($I=0$, $S=-1$), but its spin is unknown. Its closeness to the ${\bar{D}}^* \Xi _c$ threshold – $4478\,{\mathrm{MeV}}$ in the isospin-symmetric limit – suggests the molecular hypothesis as a plausible explanation for the $P_{cs}(4459)$. While in the absence of coupled-channel dynamics heavy-quark spin symmetry predicts the two spin-states of the ${\bar{D}}^* \Xi _c$ to be degenerate, power counting arguments indicate that the coupling with the nearby ${\bar{D}} \Xi _c'$ and ${\bar{D}} \Xi _c^*$ channels might be a leading order effect. This generates a hyperfine splitting in which the $J=\tfrac{3}{2}{\bar{D}}^* \Xi _c$ pentaquark will be lighter than the $J=\tfrac{1}{2}$ configuration, which we estimate to be of the order of $5-15\,{\mathrm{MeV}}$. We also point out an accidental symmetry between the $P_{cs}(4459)$ and $P_c(4440/4457)$ potentials. Finally, we argue that the spectroscopy and the $J/\psi \Lambda $ decays of the $P_{cs}(4459)$ might suggest a marginal preference for $J = \tfrac{3}{2}$ over $J = \tfrac{1}{2}$.