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

The LHCb pentaquarks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- have been theorized to be $Σ_c \bar{D}$ and $Σ_c \bar{D}^*$ 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 $Λ_c(2595) \bar{D}$ 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 $Σ_c \bar{D}^*$ and $Λ_c(2595) \bar{D}$ channels, which happens to be unusually long-ranged. The impact of the coupled-channel dynamics between the $Σ_c \bar{D}^*$ and $Λ_c(2595) \bar{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$, which will remain to be predominantly $Σ_c \bar{D}^*$ 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 $Λ_c(2595) \bar{D}$ S-wave molecule (coupled to $Σ_c \bar{D}^*$ 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.

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