Predictions for feed-down enhancements at the Λ c D ¯ and Λ c D ¯ thresholds via the triangle and box singularities

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 / ψ p and J / ψ p π , 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 also acquire contributions from both the heavier pentaquark decays and the Σ c ( * ) D ¯ ( * ) scatterings of the continuum as a feed-down phenomenon. A search for these structures in the J / ψ p and J / ψ p π spectra in both exclusive and semi-inclusive processes will provide a crucial evidence for the hadronic molecule nature of these observed pentaquarks and clarify the role played by the TS and BS in the near-threshold dynamics.