Learning pole structures of hadronic states using predictive uncertainty estimation

Physical review. D/Physical review. D., vol. 113

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 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 nonvanishing 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.

Authors 4

1. Felix Frohnert Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden

2. Denny Lane B. Sombillo

   University of the Philippines Diliman

   Affiliation as printed

   University of the Philippines Diliman

3. Evert van Nieuwenburg Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden

4. Patrick Emonts Aachen

   Leiden University · Universität Ulm · Center for Integrated Quantum Science and Technology

   Affiliation as printed

   Center for Integrated Quantum Science and Technology (IQST)

   Ulm University

   Universiteit Leiden