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

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.

Comments: 11 pages, 4 figures, 7 tables