The Bjorken sum rule with Monte Carlo and Neural Network techniques

TL;DR

This paper applies Monte Carlo and neural network techniques to parametrizing polarized deep inelastic scattering structure functions, providing unbiased, error-aware models that can inform polarized parton distribution analyses.

Contribution

It introduces a bias-free Monte Carlo and neural network approach for parametrizing polarized DIS structure functions with detailed error propagation.

Findings

Bias-free determination of structure functions with error estimates

Application to polarized DIS data for $A_1^p$ and $A_1^d$

Potential for extracting physical parameters and polarized parton distributions

Abstract

Determinations of structure functions and parton distribution functions have been recently obtained using Monte Carlo methods and neural networks as universal, unbiased interpolants for the unknown functional dependence. In this work the same methods are applied to obtain a parametrization of polarized Deep Inelastic Scattering (DIS) structure functions. The Monte Carlo approach provides a bias--free determination of the probability measure in the space of structure functions, while retaining all the information on experimental errors and correlations. In particular the error on the data is propagated into an error on the structure functions that has a clear statistical meaning. We present the application of this method to the parametrization from polarized DIS data of the photon asymmetries $A_1^p$ and $A_1^d$ from which we determine the structure functions $g_1^p(x,Q^2)$ and $g_1^d(x,Q^2)$, and discuss the possibility to extract physical parameters from these parametrizations. This work can be used as a starting point for the determination of polarized parton distributions.