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

Abstract

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

Comments: Modified Eq. (38)