The Λ c⁺→ Λ π ⁺π ⁺π ⁻ reaction, and a triangle singularity producing the Σ ^*(1430) state

We study the decay Λ c⁺ → Λ π ⁺ π ⁺ π ⁻ Λ c + → Λ π + π + π - , focusing on the production of the Σ ^*(1430) Σ ∗ ( 1430 ) resonance observed by the Belle Collaboration. Interpreted as a dynamically generated state from meson-baryon interactions in the chiral unitary approach, the Σ ^*(1430) Σ ∗ ( 1430 ) signal is shown to be enhanced by a triangle singularity involving intermediate K*- K ∗ - , p , and K̄⁰ K ¯ 0 states. This mechanism leads to a sharp peak near 1434 MeV in the π ⁺ Λ π + Λ invariant mass distribution, in agreement with the experimental observations, and predicts a secondary peak around 1875 MeV in the π ⁻ Σ ^*(1430) π - Σ ∗ ( 1430 ) spectrum tied to the triangle singularity. We also estimate the branching ratio of Λ c⁺ → π ⁺ π ⁻ Σ ^*(1430) Λ c + → π + π - Σ ∗ ( 1430 ) to be about 3.5 × 10⁻⁴ 3.5 × 10 - 4 . The results for the branching ratio and the π ⁻ Σ ^*(1430) π - Σ ∗ ( 1430 ) mass distributions are predictions of the theoretical approach, which could be tested with reanalysis of existing data.