# One pion exchange and the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks

## TL;DR

This paper investigates the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks, showing that including one pion exchange potential alters their interpreted spin-parity assignments, highlighting the need for more refined models.

## Contribution

The study demonstrates that accounting for one pion exchange potential changes the preferred quantum number assignments of the pentaquarks, challenging previous contact-range effective field theory conclusions.

## Key findings

- One pion exchange potential affects pentaquark quantum number assignments.
- Cutoff dependence indicates the need for higher-order corrections.
- Refined models are necessary to clarify pentaquark spectroscopy.

## Abstract

The LHCb collaboration has recently discovered three pentaquark-like states --- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ --- close to the $\bar{D} \Sigma_c$ and the $\bar{D}^* \Sigma_c$ meson-baryon thresholds. The standard interpretation is that they are heavy antimeson-baryon molecules. Their quantum numbers have not been determined yet, which implies two possibilities for the $P_c(4440)$ and $P_c(4457)$: $J^P = \tfrac{1}{2}^{-}$ and $J^P = \tfrac{3}{2}^{-}$. The preferred interpretation within a contact-range effective field theory is that the $P_c(4440)$ is the $J^P = \tfrac{1}{2}^-$ molecule, while the $P_c(4457)$ is the $J^P = \tfrac{3}{2}^-$ one. Here we show that when the one pion exchange potential between the heavy-antimeson and heavy-baryon is taken into account, this conclusion changes, with the contrary identification being as likely as the original one. The identification is however cutoff dependent, which suggests that improvements of the present description (e.g. the inclusion of subleading order corrections, like two-pion exchanges) are necessary in order to disambiguate the spectroscopy of the molecular pentaquarks.