Search for the ${\Sigma }^{\ast }$ state in ${\Lambda }_c^{+}\to {\pi }^{+}{\pi }^0{\pi }^{-}{\Sigma }^{+}$ decay by triangle singularity

Abstract

A ${\Sigma }^{\ast }$ resonance with spin-parity $J^P=1/2^{-}$ and mass in the vicinity of the $\bar{K}N$ threshold has been predicted in the unitary chiral approach and inferred from the analysis of CLAS data on the $\gamma p\to K^{+}{\pi }^0{\Sigma }^0$ reaction. In this work, based on the dominant Cabibbo favored weak decay mechanism, we perform a study of ${\Lambda }_c^{+}\to {\pi }^{+}{\pi }^0{\Sigma }^{\ast }$ with the possible ${\Sigma }^{\ast }$ state decaying into ${\pi }^{-}{\Sigma }^{+}$ through a triangle diagram. This process is initiated by ${\Lambda }_c^{+}\to {\pi }^{+}{\bar{K}}^{\ast }N$, then the ${\bar{K}}^{\ast }$ decays into $\bar{K}\pi$ and $\bar{K}N$ produce the ${\Sigma }^{\ast }$ through a triangle loop containing ${\bar{K}}^{\ast }N\bar{K}$ which develops a triangle singularity. We show that the ${\pi }^{-}{\Sigma }^{+}$ state is generated from final state interaction of $\bar{K}N$ in $S$-wave and isospin $I=1$, and the ${\Lambda }_c^{+}\to {\pi }^{+}{\pi }^0{\pi }^{-}{\Sigma }^{+}$ decay can be used to study the possible ${\Sigma }^{\ast }$ state around the $\bar{K}N$ threshold. The proposed decay mechanism can provide valuable information on the nature of the ${\Sigma }^{\ast }$ resonance and can in principle be tested by facilities such as LHCb, BelleII and BESIII.

Comments: Version published in PLB