Selected open-charm decays of the narrow \(P_c\) states: Quark-interchange predictions and pion-exchange sensitivity

The proximity of the narrow $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ structures to the $Σ_c\bar D^{(*)}$ thresholds motivates their interpretation as hadronic molecules. We treat the $P_c(4312)$ as an $S$-wave $Σ_c\bar D$ state with $J^P=1/2^-$ and examine both $J^P=1/2^-$ and $3/2^-$ $Σ_c\