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

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 ${\Lambda }_c{\bar{D}}_s^{(\ast )}-{\Xi }_c{\bar{D}}^{(\ast )}$ 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.

Comments: 10 Pages, 3 figures, and 6 Tables