Decay properties of $P_c$ states through the Fierz rearrangement

Abstract

We systematically study hidden-charm pentaquark currents with the quark configurations $[\bar{c}u][udc]$, $[\bar{c}d][uuc]$, and $[\bar{c}c][uud]$. Some of their relations are derived using the Fierz rearrangement of the Dirac and color indices, and the obtained results are used to study strong decay properties of $P_c$ states as ${\bar{D}}^{(\ast )}{\Sigma }_c$ hadronic molecules. We calculate their relative branching ratios for the $J/\psi p$, ${\eta }_{c}p$, ${\chi }_{c0}p$, ${\chi }_{c1}p$, ${\bar{D}}^{(\ast )0}{\Lambda }_c^{+}$, ${\bar{D}}^0{\Sigma }_c^{+}$, and ${\bar{D}}^{-}{\Sigma }_c^{++}$ decay channels. We propose to search for the $P_c(4312)$ in the ${\eta }_{c}p$ channel and the $P_c(4440)/P_c(4457)$ in the ${\bar{D}}^0{\Lambda }_c^{+}$ channel.

arXiv comment18 pages, 3 figures, 1 table, to be published in EPJC

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• Strong decays of $P_{\psi }^N(4312{)}^{+}$ to $J/\psi ({\eta }_c)p$ and ${\bar{D}}^{(\ast )}{\Lambda }_c$ within the Bethe-Salpeter framework
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• Relations between strong decay widths of the $P_c$ pentaquarks in the SU(4) flavor-spin model
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• Observation of ${\Lambda }_b^0\to {\Lambda }_c^{+}{\bar{D}}^{(\ast )0}{K}^{-}$ and ${\Lambda }_b^0\to {\Lambda }_c^{+}{D}_s^{\ast -}$ decays
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