  In this study, the impact of triangle singularity is investigated in the
isospin-breaking process $J/\psi \to \Lambda \bar{\Lambda} \pi$. The triangle
singularity is found to play a significant role in the process, resulting in
the creation of a resonance-like structure around 1.4 GeV in the
$\Lambda\pi(\bar{\Lambda}\pi)$ invariant mass spectrum. To amplify the impact
of this triangle singularity, the presence of two $\Sigma^*(\frac{1}{2}^-)$
states around 1.4 GeV and 1.6 GeV is essential, yet these states have not been
definitively identified in the current baryon spectrum. We recommend that
experiments, particularly the Beijing Spectrometer (BESIII) and the future
Super Tau-Charm Factory (STCF), to investigate the process $J/\psi \to \Lambda
\bar{\Lambda} \pi$ to offer direct evidences for our predicted triangle
singularity and additional evidence regarding the $\Sigma(\frac{1}{2}^-)$
states.
