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

TL;DR

This paper investigates the internal structure of the Pc(4457) pentaquark, proposing it may be a double peak with two different states due to coupled-channel effects involving $ ext{Lambda}_c(2595) ar{D}$ and $ ext{Sigma}_c ar{D}^*$ components, using effective field theories.

Contribution

It introduces a novel analysis of the Pc(4457) structure considering coupled-channel dynamics with effective field theories, suggesting a possible double-peak nature.

Findings

Coupled-channel effects are modest for Pc(4440) and Pc(4457), which remain mainly $ ext{Sigma}_c ar{D}^*$ molecules.

If Pc(4457) has $J^P=1/2^-$, it may include a $ ext{Lambda}_c(2595) ar{D}$ component, forming a second state.

The double-peak structure hypothesis could explain the observed properties of Pc(4457).

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 $\Sigma_c \bar{D}^*$ 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 $\Sigma_c \bar{D}^*$ and $\Lambda_c(2595) \bar{D}$ channels, which happens to be unusually long-ranged. The impact of the coupled-channel dynamics between the $\Sigma_c \bar{D}^*$ 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 $\Sigma_c \bar{D}^*$ 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 $\Sigma_c \bar{D}^*$ 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.