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.

Version published in PLB

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Cited by in corpus (14)

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• Visible narrow cusp structure in ${\Lambda }_c^{+}\to p{K}^{-}{\pi }^{+}$ enhanced by triangle singularity
• Theoretical study of the $\Omega (2012)$ state in the ${\Omega }_c^0\to {\pi }^{+}\Omega (2012{)}^{-}\to {\pi }^{+}(\bar{K}\Xi {)}^{-}$ and ${\pi }^{+}(\bar{K}\Xi \pi {)}^{-}$ decays
• Review of the low-lying excited baryons ${\Sigma }^{\ast }(1/2^{-})$
• Toward discovering the excited $\Omega$ baryons through nonleptonic weak decays of ${\Omega }_c$
• Evidence of the low-lying baryon ${\Sigma }^{\ast }(1/2^{-})$ in the process ${\Lambda }_c^{+}\to \eta {\pi }^{+}\Lambda$
• Roles of $a_0(980)$, $\Lambda (1670)$, and $\Sigma (1385)$ in the ${\Lambda }_c^{+}\to \eta \Lambda {\pi }^{+}$ decay
• Theoretical study of $N(1535)$ and ${\Sigma }^{\ast }(1/2^{-})$ in the Cabibbo-favored process ${\Lambda }_c^{+}\to p{\bar{K}}^0\eta$
• New insights into the pole parameters of the $\Lambda (1380)$, the $\Lambda (1405)$ and the $\Sigma (1385)$
• Study ${\Xi }_c^{+}\to \Lambda {\bar{K}}^0{\pi }^{+}$ and search for the low-lying baryons $\Xi (1/2^{-})$ and $\Sigma (1/2^{-})$
• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$
• Role of ${\Sigma }^{\ast }(1/2^{-})$ baryons in ${\Lambda }_c\to \Lambda {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Search for the low-lying excited baryon ${\Sigma }^{\ast }(1/2^{-})$ through process ${\Lambda }_c^{+}\to \Lambda K^0{\pi }^{+}$