Search for the (1380) 1/2^- state in ^+c ^+ decay by triangle singularity

In this work, we investigate the resonance production in ^+c ^+ decay through the triangle singularity (TS) mechanism, within an effective Lagrangian approach. We find that the appropriate loop decay process could develop a triangle singularity in the invariant mass M_ around 1. 35 GeV, with the shape depending on the quantum numbers of ^* states that couple to the final system. Especially, the (1380) 1/2^- state newly predicted in the pentaquark model, if exists, significantly enhances the TS contribution and sharpens the TS peak due to the S-wave ^* vertex in the loop. Therefore, the existence of the (1380) 1/2^- state can be examined by measuring the TS signal in ^+c ^+. Considering also possible tree-level diagrams, we additionally obtain the branching ratio Br (^+c ^+) 1. 5 10^-5. We suggest the investigation of this reaction by future BESIII, LHCb, and Belle experiments.