Machine Learning Parameterization of the Proton's Spin Structure Function*

Machine Learning (ML) provides a method for accurate parameterizations of observables with uncertainty quantification. By designing an ML model and training it on spin structure data from lepton-nucleon scattering, we seek to develop a parameterization that captures the different behaviors of the proton at low-energy and high-energy scales. Existing theoretical models often focus on constructing a proton out of its constituent quarks, which works well for high-energy scales where perturbative QCD holds. However, these theories break down at low-energy scales, resulting in inaccurate descriptions of data. This regime is where phenomenological models and parameterizations prove invaluable, however, these often rely on assumptions of function form, have incompletely quantified uncertainties, and struggle to connect the two, distinct energy scales. Therefore, using an ML architecture agnostic of functional form, with built-in uncertainty quantification, and spanning the two energy scales can provide a less statistically-biased approach. We present preliminary results for such an ML parameterization of the proton’s spin structure function g₁ using Gaussian Process Regression trained on world data for low and moderate Q².