Moments of Spin Structure Functions: Sum Rules and Polarizabilities

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.

10 pages, 8 figures, review article based on a talk at 2008 fall DNP meeting, to appear in International Journal of Modern Physics E

References in corpus (50)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• Measurements of the Proton and Deuteron Spin Structure Functions g1 and g2
• Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors
• Precision Determination of the Neutron Spin Structure Function g1n
• Measurement of the Spin-Dependent Structure Function $g_1(x)$ of the Proton
• Measurement of the Neutron Spin Structure Function $g_1^n$ with a Polarized ^3He Target
• Chiral Perturbation Theory and Baryon Properties
• Deep Inelastic Scattering of Polarized Electrons by Polarized ${}^3$He and the Study of the Neutron Spin Structure
• Positivity Constraints for Spin-Dependent Parton Distributions
• Measurements of the $Q^2$-Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n
• Dispersion relations in real and virtual Compton scattering
• QCD Analysis of Polarized Deep Inelastic Data and Parton Distributions
• Measurement of the Proton Spin Structure Function g1p with a Pure Hydrogen Target
• Measurement of the proton and the deuteron structure functions F2p and F2d
• Precision Measurement of the Neutron Spin Asymmetries and Spin-dependent Structure Functions in the Valence Quark Region
• Precision Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetries A2
• Spin Structure of the Nucleon - Status and Recent Results
• First measurement of the Gerasimov-Drell-Hearn integral for Hydrogen from 200 to 800 MeV
• Transverse Deformation of Parton Distributions and Transversity Decomposition of Angular Momentum
• Measurement of the $x$- and $Q^2$-Dependence of the Asymmetry $A_1$ on the Nucleon
• Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetry A2
• The GDH Sum Rule and Related Integrals
• Q^2-Dependence of the Proton's G_1 Structure Function Sum Rule
• The Q^2 evolution of the generalized Gerasimov-Drell-Hearn integral for the neutron using a He-3 target
• Spin structure of the nucleon at low energies
• Measurement of the Neutron Spin Structure Function g2n and Asymmetry A2n
• Q^2 Evolution of the Neutron Spin Structure Moments using a He-3 Target
• Measurement of the Proton Spin Structure Function $g_1(x,Q^2)$ for $Q^2$ from 0.15 to 1.6 GeV${}^2$ with CLAS
• Generalized Sum Rules for Spin-Dependent Structure Functions of the Nucleon
• QCD Sum Rule Calculation of Twist-4 Corrections to Bjorken and Ellis-Jaffe Sum Rules
• Generalized Drell-Hearn-Gerasimov Sum Rule at Order {\cal O}(p^4) in Chiral Perturbation Theory
• A lattice calculation of the nucleon's spin-dependent structure function g_2 revisited
• Spin-Dependent Twist-Four Matrix Elements from g_1 Data in the Resonance Region
• Burkhardt-Cottingham sum rule and forward spin polarizabilities in Heavy Baryon Chiral Perturbation Theory
• Determination of the Deep Inelastic Contribution to the Generalised Gerasimov-Drell-Hearn Integral for the Proton and Neutron
• Moments of the Spin Structure Functions g_1^p and g_1^d for 0.05 < Q^2 < 3.0 GeV^2
• Quark-Hadron Duality in Spin Structure Functions g1p and g1d
• Novel analysis of chiral loop effects in the generalized Gerasimov-Drell-Hearn sum rule
• Q^2-Dependence of the Neutron Spin Structure Function g_2^n at Low Q^2
• Measurement of the Generalized Forward Spin Polarizabilities of the Neutron
• Hadron structure at low Q^2
• The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon
• Proton Spin Structure in the Resonance Region
• On the Extraction of the Neutron Spin Structure Functions and the Gerasimov -- Drell -- Hearn Integral from ${}^3\overrightarrow{He}(\vec{e},e^{\prime })X$ data
• Measurement of Inclusive Spin Structure Functions of the Deuteron
• Generalized Gerasimov-Drell-Hearn Sum Rule for the Proton-Neutron Difference in Chiral Perturbation Theory
• QCD radiative and power corrections and Generalized GDH sum rules
• Quark-Hadron Duality in Neutron (3He) Spin Structure
• 3He Spin-Dependent Cross Sections and Sum Rules
• Higher twist analysis of the proton g_1 structure function

Cited by in corpus (17)

• QCD and strongly coupled gauge theories: challenges and perspectives
• The Spin Structure of the Nucleon
• New insights into the spin structure of the nucleon
• Dispersion Theory in Electromagnetic Interactions
• Measurement of the Q^2 Dependence of the Deuteron Spin Structure Function g_1 and its Moments at Low Q^2 with CLAS
• Spin and angular momentum in the nucleon
• Measurement of the 3He Spin-Structure Functions and of Neutron (3He) Spin-Dependent Sum Rules at 0.035<Q^2<0.24 GeV^2
• Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
• Measurement of the generalized spin polarizabilities of the neutron in the low $Q^2$ region
• Spin-dependent sum rules connecting real and virtual Compton scattering verified
• Moments of the neutron $g_2$ structure function at intermediate $Q^2$
• Polarized GPDs and structure functions of $\rho$ meson
• Polarizability relations across real and virtual Compton scattering processes
• The g2p Experiment: A Measurement of the Proton's Spin Structure Functions
• Axial anomaly and the delta_{LT} puzzle
• Small-x behavior of non-singlet spin structure function and Bjorken sum rule with pQCD correction up to NNLO and Higher twist correction
• Measurement of the nucleon spin structure functions for 0.01<$Q^2$<1 GeV${}^2$ using CLAS