$P_c(4457{)}^{+}$, $P_c(4440{)}^{+}$, and $P_c(4312{)}^{+}$: molecules or compact pentaquarks?

Abstract

In a chromomagnetic model, we analyse the properties of the newly observed $P_c(4457{)}^{+}$, $P_c(4440{)}^{+}$, and $P_c(4312{)}^{+}$ states. We estimate the masses of the $(uud{)}_{8_c}(c\bar{c}{)}_{8_c}$ and $(uds{)}_{8_c}(c\bar{c}{)}_{8_c}$ pentaquark states by considering the isospin breaking effects. Their values are determined by calculating mass distances from the ${\Sigma }_c^{++}{D}^{-}$ and ${\Xi }_c^{\prime +}{D}^{-}$ thresholds, respectively. It is found that the isospin breaking effects on the spectrum are small. From the uncertainty consideration and the rearrangement decay properties in a simple model, we find that it is possible to assign the $P_c(4457{)}^{+}$, $P_c(4440{)}^{+}$, and $P_c(4312{)}^{+}$ as $J^P=3/2^{-}$, $1/2^{-}$, and $3/2^{-}$ pentaquark states, respectively. The assignment in the molecule picture can be different, in particular for the $P_c(4312{)}^{+}$. The information from open-charm channels, e.g. $\mathcal{B}[P_c\to {\Sigma }_c^{++}{D}^{-}]/\mathcal{B}[P_c\to J/\psi p]$, will play an important role in distinguishing the inner structures of the $P_c$ states. Discussions and predictions based on the calculations are also given.

15 pages, 2 figures, 8 tables. Version accepted by PRD

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