Eur. Phys. J. C (2025) 85: 1086
https://doi.org/10.1140/epjc/s10052-025-14820-8

Regular Article - Theoretical Physics

The ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{\pi }^{+}{\pi }^{+}{\pi }^{-}$ reaction, and a triangle singularity producing the ${\mathrm{\Sigma }}^{\ast }(1430)$ state

¹ State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University, 510006, Guangzhou, China
² Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE), Guangdong-Hong Kong Joint Laboratory of Quantum Matter, 510006, Guangzhou, China
³ Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science, 510006, Guangzhou, China
⁴ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, 46071, Valencia, Spain
⁵ Center for Theoretical Physics, School of Physics and Optoelectronic Engineering, Hainan University, 570228, Haikou, China
⁶ School of Physics, Beihang University, 102206, Beijing, China
⁷ Department of Physics, Guangxi Normal University, 541004, Guilin, China
⁸ Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, 541004, Guilin, China

^a Song-Jing@buaa.edu.cn

Received: 4 June 2025
Accepted: 19 September 2025
Published online: 30 September 2025

Abstract

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