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

## TL;DR

This paper proposes using the decay $\\Lambda_c^+ o \\eta \\pi^+ \\Lambda$ to experimentally test for the existence of the predicted $\\Sigma^*_{1/2^-}(1380)$ resonance and distinguish it from the $\\Sigma^*(1385)$ state through decay distributions.

## Contribution

It introduces a novel experimental approach to identify the $\\Sigma^*_{1/2^-}(1380)$ resonance using decay angle and energy distributions in $\\Lambda_c^+$ decay processes.

## Key findings

- Decay distributions differ significantly between $\\Sigma^*(1385)$ and $\\Sigma^*_{1/2^-}(1380)$.
- The decay mechanism can be tested by future BESIII and Belle experiments.
- The process provides a clean environment to study these resonances.

## Abstract

A $\Sigma^*$ state with spin-parity $J^P = 1/2^-$ with mass and width around $1380$ MeV and $120$ MeV, refereed to as the $\Sigma^*_{1/2^-}(1380)$, 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 $\Sigma^*(1385)$ 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 $\Sigma^*$ resonances. In particular, we show that the decay angle and energy distributions of the $\pi^+$ are very different for $\Sigma^*(1385)$ and $\Sigma^*_{1/2^-}(1380)$. The proposed decay mechanism as well as the existence of the $\Sigma^*_{1/2^-}(1380)$ state can be checked by future BESIII and Belle experiments.