A comparison between the $P_c$ and $P_{cs}$ systems

TL;DR

This paper constructs effective potentials for $P_c$ and $P_{cs}$ states using symmetry principles, performs coupled-channel analysis, and discusses their mass shifts and possible partners, providing insights into their structure and relations.

Contribution

It introduces a coupled-channel analysis of $P_c$ and $P_{cs}$ states based on symmetry considerations, revealing the effects on their masses and predicting unobserved partners.

Findings

Coupled-channel effects are minor for $P_c$ states but significant for $P_{cs}$.

Mass of $P_{cs}(4338)$ is shifted near the $ ext{Xi}_car{D}$ threshold.

Predicted SU(3) partners of observed $P_c$ states have not yet been observed.

Abstract

We construct the effective potentials of the $P_c$ and $P_{cs}$ states based on the SU(3)$_{\text{f}}$ symmetry and heavy quark symmetry. Then we perform the coupled-channel analysis of the lowest isospin $P_c$ and $P_{cs}$ systems. The coupled-channel effects play different roles in the $P_c$ and $P_{cs}$ systems. In the $P_c$ systems, this effect gives minor corrections to the masses of the $P_c$ states. In the $P_{cs}$ system, the $\Lambda_c\bar{D}_s-\Xi_c\bar{D}$ coupling will shift the mass of the $P_{cs}(4338)$ close to the $\Xi_c\bar{D}$ threshold. The $\Lambda_c\bar{D}^{(*)}_s-\Xi_c\bar{D}^{(*)}$ coupling will also produce extra $P_{cs}$ states. We discuss the correspondence between the $P_c$ and $P_{cs}$ states. Our results prefer that the SU(3) partners of the observed $P_{c}(4312)$, $P_{c}(4440)$, and $P_{c}(4457)$ in the $P_{cs}$ system have not been found yet.