The $$\Lambda _c^+\rightarrow \Lambda \pi ^+\pi ^+\pi ^-$$ Λ c + → Λ π + π + π - reaction, and a triangle singularity producing the $$\Sigma ^*(1430)$$ Σ ∗ ( 1430 ) state

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