Search for theΣ⁡(1380)⁢1/2−state inΛ+𝑐→𝛾⁢𝜋+⁢Λdecay by triangle singularity

In this work, we investigate the resonance production in Λ+𝑐→𝛾⁢𝜋+⁢Λ 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 𝑀𝜋⁢Λ around 1.35 GeV, with the shape depending on the quantum numbers of Σ* states that couple to the final 𝜋⁢Λ system. Especially, the Σ⁡(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 Σ*⁢𝜋⁢Σ vertex in the loop. Therefore, the existence of the Σ⁡(1380)⁢1/2− state can be examined by measuring the TS signal in Λ+𝑐→𝛾⁢𝜋+⁢Λ. Considering also possible tree-level diagrams, we additionally obtain the branching ratio Br⁡(Λ+𝑐→𝛾⁢𝜋+⁢Λ)≃1.5×10−5. We suggest the investigation of this reaction by future BESIII, LHCb, and Belle experiments.