Extraction of S-matrix pole structure using deep learning

Abstract

In this paper, we demonstrate how deep learning can be used as a unified model-selection tool in the analysis of hadron-hadron scattering. We consider the problem of finding the number of poles in each unphysical Riemann sheet to reproduce the elastic πN amplitude. The model space is constructed using 35 pole-based models with a maximum of 4 poles distributed in each Riemann sheet. The uncertainty due to the limited energy resolution is included in the generation of training amplitudes. The learning of the deep neural network is initiated using the curriculum technique, achieving a final training and testing accuracies of 76.5% and 80.4%, respectively. Due to the presence of error bars on the amplitude, it is expected that the experimental data can be described by more than one model. Thus, to realize the multiple descriptions of a given experimental data in our analysis, we utilize the error bars and generate 106 inference amplitudes to be fed directly to the trained neural network. Out of the 35 models, only 4 models are identified by the trained deep neural network to describe the πN scattering data. The most favored pole structure for the πN amplitude is one pole in each nearby sheet and two poles in the remote sheet. Further numerical analyses show that the deep learning framework is also robust and does not depend on how the inference amplitudes are generated from the experimental data.