Sum Rules and Moments of the Nucleon Spin Structure Functions

Abstract

The nucleon has been used as a laboratory to investigate its own spin structure and Quantum Chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the {\it confinement} regime of the theory to its {\it asymptotic freedom} regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov-Drell-Hearn, Bjorken and Burkhardt-Cottingham). These moments are expressed in terms of an operator product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to a good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher twist contributions have been examined through the moments evolution as the moments evolution 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 calculations agree reasonably well with the first moment of the spin structure function $g_1$ at momentum transfer of 0.1 GeV${}^2$ but fail to reproduce the neutron data in the case of the generalized polarizability ${\delta }_{LT}$.

21 pages, 4 figures, review for Modern Physics Letters A. Minor modifications in text and improved quality for one figure. Corrected mistakes in section 2

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• Dispersion relations in real and virtual Compton scattering
• Precision Measurement of the Neutron Spin Asymmetries and Spin-dependent Structure Functions in the Valence Quark Region
• Quark-hadron duality in electron scattering
• Experimental determination of the evolution of the Bjorken integral at low Q^2
• Spin structure of the nucleon at low energies
• 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
• Measurement of the Generalized Forward Spin Polarizabilities of the Neutron
• The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon
• Measurement of Inclusive Spin Structure Functions of the Deuteron
• QCD radiative and power corrections and Generalized GDH sum rules
• Higher twist analysis of the proton g_1 structure function

Cited by in corpus (21)

• Nonperturbative QCD Coupling and its $\beta$ function from Light-Front Holography
• The Spin Structure of the Nucleon
• Experimental study of isovector spin sum rules
• High precision determination of the $Q^2$-evolution of the Bjorken Sum
• Bjorken Sum Rule and pQCD frontier on the move
• Nucleon spin structure and pQCD frontier on the move
• Determination of the Proton Spin Structure Functions for 0.05 < Q^2 < 5 GeV^2 using CLAS
• Moments of the Spin Structure Functions g_1^p and g_1^d for 0.05 < Q^2 < 3.0 GeV^2
• Transverse target spin asymmetry in inclusive DIS with two-photon exchange
• Target mass corrections for spin-dependent structure functions in collinear factorization
• Measurement of the 3He Spin-Structure Functions and of Neutron (3He) Spin-Dependent Sum Rules at 0.035<Q^2<0.24 GeV^2
• 3He Spin-Dependent Cross Sections and Sum Rules
• Fractional Analytic QCD beyond Leading Order
• Fractional Analytic QCD beyond Leading Order in timelike region
• Higher twists in polarized DIS and the size of the constituent quark
• A novel determination of non-perturbative contributions to Bjorken sum rule
• Nonsinglet polarized nucleon structure function in infrared-safe QCD
• Highlights and Perspectives of the JLab Spin Physics Program
• Measurement of the nucleon spin structure functions for 0.01<$Q^2$<1 GeV${}^2$ using CLAS
• The Jlab Upgrade - Studies of the Nucleon with CLAS12
• Study of spin sum rules (and the strong coupling constant at large distances)