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

A ${\mathrm{\Sigma }}^{\ast }$ resonance with spin-parity $J^P=1\mathrm{/}{2}^{-}$ 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 $\Lambda_c^+ \to \pi^+ \pi^0 \Sigma^$withthepossible$\Sigma^$statedecayinginto$\pi^- \Sigma^+$throughatrianglediagram\mathrm{.}Thisprocessisinitiatedby$ \Lambda_c^+ \to \pi^+ \bar{K}^N $,thenthe$\bar{K}^$decaysinto$\bar{K} \pi$and$\bar{K} N$producethe$\Sigma^$throughatriangleloopcontaining$\bar{K}^ N \bar{K}$whichdevelopsatrianglesingularity\mathrm{.}Weshowthatthe$\pi^- \Sigma^+$stateisgeneratedfromfinalstateinteractionof$\bar{K}N$in$S$-waveandisospin$I=1$,andthe$\Lambda_c^+ \to \pi^+ \pi^0 \pi^- \Sigma^+$decaycanbeusedtostudythepossible$\Sigma^*$statearoundthe$\bar{K}N$ threshold. The proposed decay mechanism can provide valuable information on the nature of the ${\mathrm{\Sigma }}^{\ast }$ resonance and can in principle be tested by facilities such as LHCb, BelleII and BESIII.