Learning Pole Structures of Hadronic States using Predictive Uncertainty Estimation

TL;DR

This paper introduces a machine learning method that estimates uncertainties to classify pole structures in hadronic scattering amplitudes, aiding the identification of exotic states like pentaquarks.

Contribution

It presents a novel uncertainty-aware classifier ensemble that accurately infers pole configurations from scattering data, including unseen experimental results.

Findings

Achieved 95% validation accuracy on synthetic data.

Successfully inferred a four-pole structure for the P_c(4312)^+ state.

Generalizable framework applicable to various hadronic states.

Abstract

Matching theoretical predictions to experimental data remains a central challenge in hadron spectroscopy. In particular, the identification of new hadronic states is difficult, as exotic signals near threshold can arise from a variety of physical mechanisms. A key diagnostic in this context is the pole structure of the scattering amplitude, but different configurations can produce similar signatures. The mapping between pole configurations and line shapes is especially ambiguous near the mass threshold, where analytic control is limited. In this work, we introduce an uncertainty-aware machine learning approach for classifying pole structures in $S$-matrix elements. Our method is based on an ensemble of classifier chains that provide both epistemic and aleatoric uncertainty estimates. We apply a rejection criterion based on predictive uncertainty, achieving a validation accuracy of nearly $95\%$ while discarding only a small fraction of high-uncertainty predictions. Trained on synthetic data with known pole structures, the model generalizes to previously unseen experimental data, including enhancements associated with the $P_{c\bar{c}}(4312)^+$ state observed by LHCb. In this, we infer a four-pole structure, representing the presence of a genuine compact pentaquark in the presence of a higher channel virtual state pole with non-vanishing width. While evaluated on this particular state, our framework is broadly applicable to other candidate hadronic states and offers a scalable tool for pole structure inference in scattering amplitudes.