Peaks within peaks and the possible two-peak structure of the Pc(4457): the effective field theory perspective

Abstract

The LHCb pentaquarks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- have been theorized to be ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ 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 ${\Lambda }_c(2595)\bar{D}$ component in 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 non-diagonal pion dynamics connecting the ${\Sigma }_c{\bar{D}}^{\ast }$ and ${\Lambda }_c(2595)\bar{D}$ channels, which happens to be unusually long-ranged. The impact of the coupled-channel dynamics between the ${\Sigma }_c{\bar{D}}^{\ast }$ and ${\Lambda }_c(2595)\bar{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$, which will remain to be predominantly ${\Sigma }_c{\bar{D}}^{\ast }$ 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 ${\Lambda }_c(2595)\bar{D}$ S-wave molecule (coupled to ${\Sigma }_c{\bar{D}}^{\ast }$ in 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.

Comments: 17 pages, 3 figures