The LHCb pentaquarks—the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$—have been theorized to be ${\mathrm{\Sigma }}_c\overline{D}$ and ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ S-wave molecules. Here, we explore the possibility that two of these pentaquarks—the $P_c(4440)$ and $P_c(4457)$—contain in addition a ${\mathrm{\Lambda }}_c(2595)\overline{D}$ component in the P-wave. We will analyze the effects of this extra channel within two effective field theories: the first one will be a standard contact-range effective field theory, and the second one will include the nondiagonal pion dynamics connecting the ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ and ${\mathrm{\Lambda }}_c(2595)\overline{D}$ channels, which happens to be unusually long ranged. The impact of the coupled-channel dynamics between the ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ and ${\mathrm{\Lambda }}_c(2595)\overline{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$, which will remain predominantly ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ molecules. However, if the quantum numbers of the $P_c(4457)$ are $J^P={\frac{1}{2}}^{-}$, the coupled-channel dynamics is likely to induce the binding of a $\mathrm{\Lambda }(2595)\overline{D}$ S-wave molecule (coupled to ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ in the P-wave) with $J^P={\frac{1}{2}}^{+}$ and a mass similar to the $P_c(4457)$. If this is the case, the $P_c(4457)$ could actually be a double peak containing two different pentaquark states.

• Received 10 August 2020
• Accepted 7 December 2020

DOI:https://doi.org/10.1103/PhysRevD.103.014023

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