The $Λ_c^+\toΛπ^+π^+π^-$ reaction, and a triangle singularity producing the $Σ^*(1430)$ state

Abstract

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