The pentaquark states $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ could be nicely arranged into a multiplet of seven molecules of ${\overline{D}}^{(*)}{\mathrm{\Sigma }}_c^{(*)}$ dictated by heavy quark spin symmetry. However, the spins of $P_c(4440)$ and $P_c(4457)$ are not yet fully determined. We employ the contact-range effective field theory to investigate the SU(3)-flavor counterparts of ${\overline{D}}^{(*)}{\mathrm{\Sigma }}_c^{(*)}$ and study the possibility of whether their discovery could help determine the spins of $P_c(4457)$ and $P_c(4440)$. We find the existence of a complete hidden charm strange multiplet of ${\overline{D}}^{(*)}{\mathrm{\Xi }}_c^{(\prime )*}$ molecules, irrespective of the spins of $P_c(4440)$ and $P_c(4457)$. On the other hand, we find that although molecules of ${\overline{D}}^{(*)}{\mathrm{\Xi }}_c$ are also likely, depending on the realization of the underlying dynamics, their discovery could be more useful for determining the spins of $P_c(4440)$ and $P_c(4457)$ and for telling us how heavy quark and light quark interactions depend on the spin of the light quark pair.

• Received 29 November 2020
• Accepted 13 January 2021

DOI:https://doi.org/10.1103/PhysRevD.103.034003

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society