Peaks within peaks and the possible two-peak structure of the $P_c(4457)$: the effective field theory perspective
Résumé
The LHCb pentaquarks—the Pc(4312), Pc(4440), and Pc(4457)—have been theorized to be ΣcD¯ and ΣcD¯* S-wave molecules. Here, we explore the possibility that two of these pentaquarks—the Pc(4440) and Pc(4457)—contain in addition a Λc(2595)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 ΣcD¯* and Λc(2595)D¯ channels, which happens to be unusually long ranged. The impact of the coupled-channel dynamics between the ΣcD¯* and Λc(2595)D¯ components is modest at best for the Pc(4440) and Pc(4457), which will remain predominantly ΣcD¯* molecules. However, if the quantum numbers of the Pc(4457) are JP=12-, the coupled-channel dynamics is likely to induce the binding of a Λ(2595)D¯ S-wave molecule (coupled to ΣcD¯* in the P-wave) with JP=12+ and a mass similar to the Pc(4457). If this is the case, the Pc(4457) could actually be a double peak containing two different pentaquark states.