The role of triangle singularity in isospin breaking process J/ and the possible evidence of ^* (12^-) states

In this study, the impact of triangle singularity is investigated in the isospin-breaking process J/. 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 () invariant mass spectrum. To amplify the impact of this triangle singularity, the presence of two ^* (12^-) 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/ to offer direct evidences for our predicted triangle singularity and additional evidence regarding the (12^-) states.