Hidden-charm pentaquark states through the current algebra: From their productions to decays

There may exist seven $\bar D^{(*)} \Sigma_c^{(*)}$ hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in $\Lambda_b^0$ decays through the current algebra, i.e., $\mathcal{B}(\Lambda_b^0 \to P_c K^-):\mathcal{B}(\Lambda_b^0 \to P_c^\prime K^-)$ with $P_c$ and $P_c^\prime$ two different states. We also study their decay properties through the Fierz rearrangement, and further calculate these ratios in the $J/\psi p$ mass spectrum, i.e., $\mathcal{B}(\Lambda_b^0 \to P_c K^- \to J/\psi p K^-):\mathcal{B}(\Lambda_b^0 \to P_c^\prime K^- \to J/\psi p K^-)$. Our results suggest that the $\bar D^{*} \Sigma_c^{*}$ molecular states of $J^P = 1/2^-$ and $3/2^-$ are possible to be observed in future experiments.