Pole structure of $P_\psi^N(4312)^+$ via machine learning and uniformized S-matrix

TL;DR

This study uses machine learning trained on model-independent S-matrix poles to analyze the pole structure of the $P_ extpsi^{N}(4312)^{+}$, revealing a potentially three-pole resonance with implications for its nature.

Contribution

It introduces a novel machine learning approach trained on uniformized S-matrix poles to investigate the pole structure of a hadronic state.

Findings

Five neural networks favor a three-pole structure.

Identification of a pole-shadow pair indicating a true resonance.

The observed peak mimics a hadronic molecule due to combined pole effects.

Abstract

We probed the pole structure of the $P_\psi^{N}(4312)^{+}$ using a trained deep neural network. The training dataset was generated using uniformized independent S-matrix poles to ensure that the obtained interpretation is as model-independent as possible. To prevent possible ambiguity in the interpretation of the pole structure, we included the contribution from the off-diagonal element of the S-matrix. Five out of the six neural networks we trained favor $P_\psi^{N}(4312)^{+}$ as possibly having a three-pole structure, with one pole on each of the unphysical sheets - a first in its report. The two poles can be associated to a pole-shadow pair which is a characteristic of a true resonance. On the other hand, the last pole is most likely associated with the coupled-channel effect. The combined effect of these poles produced a peak below the $\Sigma^{+}_C\bar{D}^0$ which mimic the line shape of a hadronic molecule.