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

Abstract: The proximity of the narrow $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ structures to the $Σ_c\bar D<sup>{(*)}$ thresholds motivates their interpretation as hadronic molecules. We treat the $P_c(4312)$ as an $S$-wave $Σ_c\bar D$ state with $J<sup>P=1/2<sup>-$ and examine both $J<sup>P=1/2<sup>-$ and $3/2^-$ $Σ_c\bar D<sup>*$ assignments for each heavier peak. The selected $S$-wave open-charm transitions to $Λ_c\bar D<sup>{(*)}$ are calculated at Born order in the quark-interchange model, including the prior and post rearrangement diagrams and their color, flavor, spin, and spatial matrix elements. Across the input variations considered, the quark-interchange widths robustly favor $Λ_c\bar D<sup>*$ over $Λ_c\bar D$ for every $J<sup>P=1/2<sup>-$ assignment. At either heavier peak mass, the $Λ_c\bar D<sup>*$ width for $J<sup>P=3/2<sup>-$ is suppressed by approximately one order of magnitude relative to $J<sup>P=1/2<sup>-$, providing a potential decay-based discriminator of the spin assignments. The large channel hierarchies arise from spatial overlaps and interference between spin-independent and hyperfine contributions and are not universal heavy-quark-spin-symmetry ratios. We also explore a retarded one-pion-exchange transition at first Born order. It affects $P_c(4312)\toΛ_c\bar D<sup>*$ most strongly, while the coherent widths remain sensitive to the cutoff, energy-transfer prescription, short-distance subtraction, and unresolved relative matching sign. The quark-interchange hierarchies are therefore the central predictions, whereas the pion-exchange results quantify matching sensitivity. Measurements of the $Λ_c\bar D<sup>*$ modes can directly test these patterns.