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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 standardinterpretation is that they are heavy antimeson-baryon molecules. Their quantumnumbers 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-rangeeffective 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 showthat when the one pion exchange potential between the heavy-antimeson andheavy-baryon is taken into account, this conclusion changes, with the contraryidentification being as likely as the original one. The identification ishowever cutoff dependent, which suggests that improvements of the presentdescription (e.g. the inclusion of subleading order corrections, like two-pionexchanges) are necessary in order to disambiguate the spectroscopy of themolecular pentaquarks.

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