Search for the $\Sigma(1380)1/2^-$ state in $\Lambda^+_c \to \gamma \pi^+ \Lambda$ decay by triangle singularity

TL;DR

This paper explores the potential to detect the hypothesized $ ext{Sigma}(1380)1/2^-$ state via triangle singularity effects in $ ext{Lambda}_c^+ o ext{gamma} ext{pi}^+ ext{Lambda}$ decays, proposing experimental measurements to confirm its existence.

Contribution

It introduces a novel method to identify the $ ext{Sigma}(1380)1/2^-$ state through triangle singularity signals in charmed baryon decays, linking theoretical predictions with experimental searches.

Findings

Triangle singularity appears around 1.35 GeV in $M_{\pi\Lambda}$.

The $ ext{Sigma}(1380)1/2^-$ enhances the TS peak if it exists.

Estimated branching ratio is approximately $1.5 \times 10^{-5}$.

Abstract

In this work, we investigate the resonance production in $\Lambda^+_c \to \gamma \pi^+ \Lambda$ 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 $M_{\pi\Lambda}$ around $1.35$ GeV, with the shape depending on the quantum numbers of $\Sigma^*$ states that couple to the final $\pi\Lambda$ system. Especially, the $\Sigma(1380)1/2^-$ state newly predicted in the pentaquark model, if exists, significantly enhances the TS contribution and sharpens the TS peak due to the $S$-wave $\Sigma^*\pi\Sigma$ vertex in the loop. Therefore, the existence of the $\Sigma(1380)1/2^-$ state can be examined by measuring the TS signal in $\Lambda^+_c \to \gamma \pi^+ \Lambda$. Considering also possible tree-level diagrams, we additionally obtain the branching ratio ${\rm Br}(\Lambda^+_c \to \gamma \pi^+ \Lambda)\simeq 1.5\times 10^{-5}$. We suggest the investigation of this reaction by future BESIII, LHCb, and Belle experiments.