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.
Highlights
The discovery of three pentaquark peaks—the Pcð4312Þ, Pcð4440Þ, and Pcð4457Þ—by the LHCb Collaboration [1] raises the question of what is their nature
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 Ã and
We will begin by reviewing their standard molecular interpretations as D Σc and D ΣÃc bound states, and we will move to the novel molecular interpretation in which the D Λc1 channel is included as an explicit degree of freedom for the Pcð4440Þ and Pcð4457Þ pentaquarks
Summary
The discovery of three pentaquark peaks—the Pcð4312Þ, Pcð4440Þ, and Pcð4457Þ—by the LHCb Collaboration [1] raises the question of what is their nature. It was realized that the pion-exchange dynamics mediating the D ÃΣc → D Λc1 transition is unusually long ranged and in practice takes the form of a 1=r2 potential [22]. This is a really interesting potential in the sense that it can display discrete scale invariance when attractive enough [23,24,25], which in turn opens the possibility of the existence of hadronic molecules for which there is a geometric spectrum reminiscent of the Efimov effect in the threeboson system [26].
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