Moments of Spin Structure Functions: Sum Rules and Polarizabilities

TL;DR

This paper reviews experimental and theoretical advances in understanding nucleon spin structure functions, sum rules, and polarizabilities across various momentum transfers, testing QCD predictions and effective theories.

Contribution

It provides a comprehensive analysis of spin structure moments, sum rules, and polarizabilities, integrating new data with theoretical models to test QCD and chiral theories.

Findings

Chiral perturbation theory agrees with the first moment at low Q^2

Higher moments show discrepancies with some neutron data

Burkhardt-Cottingham sum rule verified across a wide Q^2 range

Abstract

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight for some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules. These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g_1 at low momentum transfer of 0.05 - 0.1 GeV^2 but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability Delta_LT. The Burkhardt-Cottingham sum rule has been verified with good accuracy in a wide range of Q^2 assuming that no singular behavior of the structure functions is present at very high excitation energies.