Measurements of the proton and deuteron spin structure functions<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Abstract

Measurements are reported of the proton and deuteron spin structure functions ${g}_{1}^{p}$ and ${g}_{1}^{d}$ at beam energies of 29.1, 16.2, and 9.7 GeV, and ${g}_{2}^{p}$ and ${g}_{2}^{d}$ at a beam energy of 29.1 GeV. The integrals ${\ensuremath{\Gamma}}_{p}={\ensuremath{\int}}_{0}^{1}{g}_{1}^{p}{(x,Q}^{2})dx$ and ${\ensuremath{\Gamma}}_{d}={\ensuremath{\int}}_{0}^{1}{g}_{1}^{d}{(x,Q}^{2})dx$ were evaluated at fixed ${Q}^{2}=3(\mathrm{GeV}{/c)}^{2}$ using the full data set to yield ${\ensuremath{\Gamma}}_{p}=0.132\ifmmode\pm\else\textpm\fi{}0.003(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.009(\mathrm{syst})$ and ${\ensuremath{\Gamma}}_{d}=0.047\ifmmode\pm\else\textpm\fi{}0.003\ifmmode\pm\else\textpm\fi{}0.006.$ The ${Q}^{2}$ dependence of the ratio ${g}_{1}{/F}_{1}$ was studied and found to be small for ${Q}^{2}&gt;1(\mathrm{GeV}{/c)}^{2}.$ Within experimental precision the ${g}_{2}$ data are well described by the twist-2 contribution, ${g}_{2}^{\mathrm{WW}}.$ Twist-3 matrix elements were extracted and compared to theoretical predictions. The asymmetry ${A}_{2}$ was measured and found to be significantly smaller than the positivity limit $\sqrt{R}$ for both proton and deuteron targets. ${A}_{2}^{p}$ is found to be positive and inconsistent with zero. Measurements of ${g}_{1}$ 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 integrals ${\ensuremath{\Gamma}}_{p}$ and ${\ensuremath{\Gamma}}_{n}$ below the scaling region.