${\Sigma }_{1/2^{-}}^{\ast }(1380)$ in the ${\Lambda }_c^{+}\to \eta {\pi }^{+}\Lambda$ decay

Abstract

A ${\Sigma }^{\ast }$ state with spin-parity $J^P=1/2^{-}$ with mass and width around $1380$ MeV and $120$ MeV, refereed to as the ${\Sigma }_{1/2^{-}}^{\ast }(1380)$, has been predicted in several pentaquark models and inferred from the analysis of CLAS $\gamma p$ data. In the present work, we discuss how one can employ the ${\Lambda }_c^{+}\to \eta {\pi }^{+}\Lambda$ decay to test its existence, as well as to study the ${\Sigma }^{\ast }(1385)$ state with $J^P=3/2^{+}$. Because the final ${\pi }^{+}\Lambda$ system is in a pure isospin $I=1$ combination, the ${\Lambda }_c^{+}\to \eta {\pi }^{+}\Lambda$ decay can be an ideal process to study these ${\Sigma }^{\ast }$ resonances. In particular, we show that the decay angle and energy distributions of the ${\pi }^{+}$ are very different for ${\Sigma }^{\ast }(1385)$ and ${\Sigma }_{1/2^{-}}^{\ast }(1380)$. The proposed decay mechanism as well as the existence of the ${\Sigma }_{1/2^{-}}^{\ast }(1380)$ state can be checked by future BESIII and Belle experiments.

Comments: 6 pages, 7 figures