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Measurements of the Proton and Deuteron Spin Structure Functions g1 and g2

E143 collaboration

TL;DR

This work provides comprehensive measurements of the proton and deuteron spin structure functions g1 and g2 across deep-inelastic and resonance kinematics. It confirms a small Q^2 dependence of g1/F1 for Q^2 > 1 GeV^2, finds g2 consistent with the Wandzura-Wilczek twist-2 expectation within uncertainties, and extracts twist-3 contributions. The first moments Γ1 show general agreement with the Bjorken sum rule while Ellis-Jaffe predictions are slightly violated, implying nonzero strange and/or gluon spin contributions. Resonance-region data reveal clear structure consistent with known γ*N→N* amplitudes, and the overall results support a spin composition of the nucleon where quark spins account for a modest fraction while gluons and orbital angular momentum play important roles. Collectively, these measurements provide stringent tests of QCD in spin phenomena and set the stage for determining the gluon spin distribution in future work.

Abstract

Measurements are reported of the proton and deuteron spin structure functions g1 at beam energies of 29.1, 16.2, and 9.7 GeV and g2 at a beam energy of 29.1 GeV. The integrals of g1 over x have been evaluated at fixed Q**2 = 3 (GeV/c)**2 using the full data set. The Q**2 dependence of the ratio g1/F1 was studied and found to be small for Q**2 > 1 (GeV/c)**2. Within experimental precision the g2 data are well-described by the Wandzura-Wilczek twist-2 contribution. Twist-3 matrix elements were extracted and compared to theoretical predictions. The asymmetry A2 was measured and found to be significantly smaller than the positivity limit for both proton and deuteron targets. A2 for the proton is found to be positive and inconsistent with zero. Measurements of g1 in the resonance region show strong variations with x and Q**2, consistent with resonant amplitudes extracted from unpolarized data. These data allow us to study the Q**2 dependence of the first moments of g1 below the scaling region.

Measurements of the Proton and Deuteron Spin Structure Functions g1 and g2

TL;DR

This work provides comprehensive measurements of the proton and deuteron spin structure functions g1 and g2 across deep-inelastic and resonance kinematics. It confirms a small Q^2 dependence of g1/F1 for Q^2 > 1 GeV^2, finds g2 consistent with the Wandzura-Wilczek twist-2 expectation within uncertainties, and extracts twist-3 contributions. The first moments Γ1 show general agreement with the Bjorken sum rule while Ellis-Jaffe predictions are slightly violated, implying nonzero strange and/or gluon spin contributions. Resonance-region data reveal clear structure consistent with known γ*N→N* amplitudes, and the overall results support a spin composition of the nucleon where quark spins account for a modest fraction while gluons and orbital angular momentum play important roles. Collectively, these measurements provide stringent tests of QCD in spin phenomena and set the stage for determining the gluon spin distribution in future work.

Abstract

Measurements are reported of the proton and deuteron spin structure functions g1 at beam energies of 29.1, 16.2, and 9.7 GeV and g2 at a beam energy of 29.1 GeV. The integrals of g1 over x have been evaluated at fixed Q**2 = 3 (GeV/c)**2 using the full data set. The Q**2 dependence of the ratio g1/F1 was studied and found to be small for Q**2 > 1 (GeV/c)**2. Within experimental precision the g2 data are well-described by the Wandzura-Wilczek twist-2 contribution. Twist-3 matrix elements were extracted and compared to theoretical predictions. The asymmetry A2 was measured and found to be significantly smaller than the positivity limit for both proton and deuteron targets. A2 for the proton is found to be positive and inconsistent with zero. Measurements of g1 in the resonance region show strong variations with x and Q**2, consistent with resonant amplitudes extracted from unpolarized data. These data allow us to study the Q**2 dependence of the first moments of g1 below the scaling region.

Paper Structure

This paper contains 62 sections, 57 equations, 25 figures, 38 tables.

Table of Contents

  1. Introduction
  2. Interpretation and Theory
  3. Formalism
  4. The Deep-Inelastic Spin Structure Function $g_1(x,Q^2)$
  5. The Quark-Parton Model
  6. Perturbative QCD and the Role of the Gluons
  7. The Bjorken Sum Rule
  8. The Ellis-Jaffe Sum Rule
  9. $Q^2$ Dependence: Evolution and Higher Twist
  10. The Deep-Inelastic Spin Structure Function $g_2(x,Q^2)$
  11. Physical Interpretation
  12. OPE Sum Rules and the Twist-3 Matrix Element
  13. The Burkhardt-Cottingham Sum Rule
  14. Target Mass Effects
  15. Resonance Region Polarized Structure Functions
  16. ...and 47 more sections

Figures (25)

  • Figure 1: The layout of the lasers and the polarized electron gun at the accelerator injector is shown schematically. Two types of lasers are used, one for the SLC, which produces two 2 nsec pulses separated by 61 nsec, and one for the fixed target experiments, which produces one pulse 2 $\mu$sec long.
  • Figure 2: The layout of the Mø ller polarimeter systems used in the E143 experiment (not to scale).
  • Figure 3: (a) A typical Mø ller coincidence event time difference spectrum. (b)-(c) Two views of the distribution of coincidence events in the 7$\times$7=49 possible combinations. View (c) shows the hidden back-side of view (b). True Mø ller events were constrained to occur in the crest.
  • Figure 4: Typical measured single-arm Mø ller line-shapes in detector 7 at 29.1 GeV. The (R+L) data (points), (R+L) fit (histogram), and (R+L) background (shaded region) are plotted in (a) versus the relative y position of the channel. The (R--L) data (points) and (R--L) background (shaded region) are plotted in (b).
  • Figure 5: Variation of the quantum efficiency (QE) of the polarized source over the course of the E143 experiment.
  • ...and 20 more figures