Predictions for feed-down enhancements at the $Λ_c \bar{D}$ and $Λ_c \bar{D}^*$ thresholds via the triangle and box singularities

Abstract

We demonstrate that triangle singularity (TS) and box singularity (BS) mechanisms can produce unique narrow enhancements at the Λ c D and Λ c D * thresholds in the invariant mass spectra of J/ψp and J/ψpπ, respectively. Taking into account that such mechanisms only depend on the initial Σ ( * ) c D( * ) interactions near threshold within the TS or BS kinematic regimes, the Λ c D and Λ c D * threshold enhancements can be regarded as a feeddown phenomenon originated from both the heavier pentaquark decays and the Σ ( * ) c D( * ) scatterings from the continuum. A search for these structures in the J/ψp and J/ψpπ spectra in both exclusive and semi-inclusive processes will provide a smoking-gun evidence for the hadronic molecule nature of those observed pentaquarks and clarify the role played by the TS and BS in the near-threshold dynamics. c D( * ) channel, they were interpreted as hadronic molecules formed by the Σ ( * ) c D( * ) near-threshold interactions [13-23]. With the Run-2 data samples, the reanalysis of Λ 0 b → J/ψpK − exposes more detailed structures in the J/ψp invariant mass spectrum [24]. P c (4450) splits into two states, P c (4440) and P c (4457), which fit well the J P = 1/2 − and 3/2 − doublet formed by Σ c D * , and a new state P c (4312), which fits the Σ c D molecular state, is identified [25-35]. Meanwhile, signals for P c (4380), formerly assigned as the Σ *c D molecule in the Run-1 analysis, become obscure in the Run-2 analysis. It turns out to be broad and can be even absorbed by the background [24]. It should be noted that the quantum numbers determined by the Run-2 analysis are more consistent with the molecular scenario based on the relative S -wave interactions and also consistent with the early theoretical predictions [36][37][38][39].A key issue clarified by the Run-2 analysis is that these hidden charmonium pentaquark candidates couple to the nearby Σ c D( * ) in a relative S -wave. This makes the hadronic molecule scenario a natural interpretation for their internal structures and provide important insights into the threshold dynamics. Note that these observed P c states are correlated with the Σ ( * ) c D( * ) thresholds instead of Λ ( * ) c D( * ) . It is also interesting to observe that this feature seems to be consistent with the one boson exchange (OBE) dynamics between the charmed meson and baryon. Namely, it manifests to be attractive between Σ ( * ) c and D( * ) , but appears to be repulsive between Λ ( * ) c