Model Selection for Pion Photoproduction

TL;DR

This paper introduces a novel approach using LASSO and information criteria for model selection in pion photoproduction analysis, aiming to improve the accuracy and efficiency of partial-wave analysis in hadron spectroscopy.

Contribution

It applies LASSO combined with information theory and cross-validation to pion photoproduction, a method not widely used in excited hadron analysis, demonstrating its feasibility with real data.

Findings

LASSO effectively selects minimal yet sufficient models.

Method improves fit quality in low-energy pion photoproduction.

Demonstrated applicability with experimental data.

Abstract

Partial-wave analysis of meson and photon-induced reactions is needed to enable the comparison of many theoretical approaches to data. In both energy-dependent and independent parametrizations of partial waves, the selection of the model amplitude is crucial. Principles of the $S$-matrix are implemented to different degree in different approaches, but a many times overlooked aspect concerns the selection of undetermined coefficients and functional forms for fitting, leading to a minimal yet sufficient parametrization. We present an analysis of low-energy neutral pion photoproduction using the Least Absolute Shrinkage and Selection Operator (LASSO) in combination with criteria from information theory and $K$-fold cross validation. These methods are not yet widely known in the analysis of excited hadrons but will become relevant in the era of precision spectroscopy. The principle is first illustrated with synthetic data, then, its feasibility for real data is demonstrated by analyzing the latest available measurements of differential cross sections ($d\sigma/d\Omega$), photon-beam asymmetries ($\Sigma$), and target asymmetry differential cross sections ($d\sigma_T/d\Omega$) in the low energy regime.