Revisiting the $\Lambda (1405)$ pole structure with convolutional neural networks

Abstract

We revisit the long-standing ambiguity surrounding the complex pole structure of the $\Lambda (1405)$ resonance by reframing it as a classification problem for convolutional neural networks (CNNs). By training our models to recognize subtle geometric variations on nearly degenerate lineshapes using targeted differential feature on empirical CLAS data, we establish a data-driven consensus on large inference samples. Our results show that the analytic structure characterized by two poles on the $[bt]$ sheet and additional pole on the $[bb]$ sheet globally dominates. The inference-guided pole parameter extraction reveals that the $\Lambda (1405)$ is a two-state system, characterized by a molecular state sitting below the $\bar{K}N$ threshold and a non-molecular state lying above the $\Sigma \pi$ threshold.

14 pages, 5 figures, comments are welcome