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 $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ and the ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ 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 ${P}_{c}(4457)$: ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$. The preferred interpretation within a contact-range effective field theory is that the ${P}_{c}(4440)$ is the ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ molecule, while the ${P}_{c}(4457)$ is the ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$ 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.
Highlights
The Pcð4312Þ, Pcð4440Þ and Pcð4457Þ are three hiddencharm pentaquark-like states recently discovered by the LHCb collaboration [1]
As we will see the inclusion of pions will be able to change the preferred quantum number identification of the Pcð4440Þ and Pcð4457Þ pentaquarks
II we review how Heavy-quark spin symmetry (HQSS) applies to heavy baryon-meson molecules, in which we advocate the use of a particular notation—the light-quark notation [29]—for the description of the contact range and the One pion exchange (OPE) potential within effective field theory (EFT)
Summary
The Pcð4312Þ, Pcð4440Þ and Pcð4457Þ are three hiddencharm pentaquark-like states recently discovered by the LHCb collaboration [1]. Owing to their closeness to the D Σc and D ÃΣc thresholds, they have been theorized to be. Pcð4312Þ is a D Σc molecule and the Pcð4440Þ and Pcð4457Þ are D ÃΣc molecules This interpretation unambiguously predicts the quantum numbers of the Pcð4312Þ to be JP 1⁄4 12−. Checking which quantum number corresponds to each one of these two pentaquarks is important to clarify their nature, in particular when confronted with future experimental measurements of their properties. From the recent theoretical models for the spectroscopy and decays of these two molecules, the preferred identification so far seems to be. Ref. [18] proposed a contact-range EFT to describe the D Σc molecular states, which was used to predict a 5− 2
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