Model independent analysis of coupled-channel scattering: a deep learning approach

TL;DR

This paper presents a deep learning method to analyze coupled-channel scattering amplitudes, accurately extracting pole configurations while accounting for experimental errors, demonstrating robustness and independence from data sampling methods.

Contribution

It introduces a novel deep neural network approach that incorporates statistical errors and uses a curriculum method to reliably identify pole configurations in scattering amplitudes.

Findings

Successfully applied to $\pi N$ amplitude data

Identified poles causing amplitude enhancements

Demonstrated robustness against data sampling variations

Abstract

We develop a robust method to extract the pole configuration of a given partial-wave amplitude. In our approach, a deep neural network is constructed where the statistical errors of the experimental data are taken into account. The teaching dataset is constructed using a generic S-matrix parametrization, ensuring that all the poles produced are independent of each other. The inclusion of statistical error results into a noisy classification dataset which we should solve using the curriculum method. As an application, we use the elastic $\pi N$ amplitude in the $I(J^P)=1/2(1/2^{-})$ sector where $10^6$ amplitudes are produced by combining points in each error bar of the experimental data. We fed the amplitudes to the trained deep neural network and find that the enhancements in the $\pi N$ amplitude are caused by one pole in each nearby unphysical sheet and at most two poles in the distant sheet. Finally, we show that the extracted pole configurations are independent of the way points in each error bar are drawn and combined, demonstrating the statistical robustness of our method.