A Deep Learning Framework for Disentangling Triangle Singularity and Pole-Based Enhancements

Enhancements in the invariant mass distribution or scattering cross-section are usually associated with resonances. However, the nature of exotic signals found near hadron-hadron thresholds remain a puzzle today due to the presence of experimental uncertainties. In fact, a purely kinematical triangle diagram is also capable of producing similar structures, but do not correspond to any unstable quantum state. In this paper, we report for the first time, that a deep neural network can be trained to distinguish triangle singularity from pole-based enhancements with a reasonably high accuracy of discrimination between the two seemingly identical line shapes. We also identify the type of triangle enhancement that can be misidentified as a dynamic pole structure. We apply our method to confirm that the $P_ψ^N(4312)^+$ state is not due to a triangle singularity, but is more consistent with a pole-based interpretation, as determined solely through pure line-shape analysis. Lastly, we explain how our method can be used as a model-selection framework useful in studying other exotic hadron candidates.