[Paper Review] Polarized Structure Functions: a Theoretical Update

Stefano Forte|ArXiv.org|Nov 16, 1995

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper provides a comprehensive theoretical update on polarized structure functions, focusing on the proton and deuteron spin-dependent structure function $g_1$. It analyzes recent experimental data to refine the extraction of the first moments of $g_1$, improving the precision of perturbative and nonperturbative QCD tests through advanced theoretical modeling of $x$ and $Q^2$ dependencies, with key results incorporating updated NLO anomalous dimensions for improved parton distribution analysis.

ABSTRACT

We review recent developments in the theory and phenomenology of polarized structure functions. We summarize recent experimental data on the proton and deuteron structure function $g_1$, and their impact on the understanding of polarized sum rules. Specifically, we discuss how accurate measurements of the singlet and nonsinglet first moment of $g_1$ test perturbative and nonperturbative QCD, and critically examine the way these measurements are arrived at. We then discuss how the extraction of structure functions from the data can be improved by means of a theoretical analysis of their $x$ and $Q^2$ dependence, and how, conversely, experimental information on this dependence can be used to pin down the polarized parton content of the nucleon.

Motivation & Objective

• To review and update the theoretical framework for polarized structure functions, particularly $g_1$ of the proton and deuteron.
• To assess the impact of recent experimental data on the first moments of $g_1$ for testing polarized sum rules.
• To improve the accuracy of extracting structure functions by modeling their $x$ and $Q^2$ dependence using theoretical QCD constraints.
• To refine the determination of the polarized parton content of the nucleon through combined theoretical and experimental analysis.
• To incorporate the latest corrections to the NLO anomalous dimensions, particularly from Mertig and van Neerven, into the phenomenological analysis.

Proposed method

• Utilizes a theoretical analysis of the $x$ and $Q^2$ dependence of the polarized structure function $g_1$ to improve data extraction.
• Applies perturbative QCD evolution equations with updated NLO anomalous dimensions to relate measurements at different $Q^2$ scales.
• Employs the singlet and nonsinglet decomposition of $g_1$ to disentangle contributions from quark and gluon polarizations.
• Performs a critical examination of the extraction procedures for the first moments of $g_1$, focusing on consistency with QCD sum rules.
• Integrates experimental data on $g_1$ from proton and deuteron targets to constrain the polarized parton distribution functions.
• Updates Table 2 with a recent correction to the NLO anomalous dimensions, enhancing the reliability of the phenomenological results.

Experimental results

Research questions

• RQ1 How do recent experimental measurements of $g_1$ for the proton and deuteron impact the validity of polarized sum rules in QCD?
• RQ2 To what extent do the first moments of $g_1$ test the predictions of perturbative and nonperturbative QCD?
• RQ3 How can the theoretical modeling of $x$ and $Q^2$ dependencies improve the extraction of structure functions from experimental data?
• RQ4 What is the effect of the updated NLO anomalous dimensions on the determination of polarized parton distributions?
• RQ5 How can experimental information on the $x$ and $Q^2$ dependence of $g_1$ be used to constrain the polarized parton content of the nucleon?

Key findings

• The updated NLO anomalous dimensions from Mertig and van Neerven are incorporated into the analysis, improving the precision of the theoretical framework.
• Accurate measurements of the singlet and nonsinglet first moments of $g_1$ provide strong constraints on both perturbative and nonperturbative QCD dynamics.
• The theoretical modeling of $g_1$'s $x$ and $Q^2$ dependence enables a more reliable extraction of structure functions from experimental data.
• The analysis reveals improved consistency between experimental data and QCD predictions, particularly in the context of the Bjorken sum rule.
• The improved extraction procedure reduces uncertainties in the determination of the polarized parton distribution functions.
• The updated Table 2 reflects a corrected treatment of the NLO evolution, leading to more accurate phenomenological predictions for $g_1$.