The $P_{cs}(4459)$ pentaquark from a combined effective field theory and phenomenological perspective

Abstract

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 ${\bar{D}}^{\ast }{\Xi }_c$ 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 ${\bar{D}}^{\ast }{\Xi }_c$ to be degenerate, power counting arguments indicate that the coupling with the nearby $\bar{D}{\Xi }_c^{\prime }$ and $\bar{D}{\Xi }_c^{\ast }$ channels might be a leading order effect. This generates a hyperfine splitting in which the $J=\frac{3}{2}$ ${\bar{D}}^{\ast }{\Xi }_c$ pentaquark will be lighter than the $J=\frac{1}{2}$ 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 $J=\frac{3}{2}$ over $J=\frac{1}{2}$.

Comments: 16 pages, 1 figure; includes discussions on power counting, the J=1/2,3/2 hyperfine splitting, saturation, phenomenological relation between the Pcs(4459) and Pc(4440/4457) potentials, decay to $J/\psi \Lambda$, etc