Measurements of the proton and deuteron spin structure functions $g_1$ and $g_2$

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 ${\Gamma }_p={\int }_0^1{g}_1^p{(x,Q}^2)dx$ and ${\Gamma }_d={\int }_0^1{g}_1^d{(x,Q}^2)dx$ were evaluated at fixed $Q^2=3\mathrm{}(\mathrm{GeV}{/c)}^2$ using the full data set to yield ${\Gamma }_p=0.132\pm 0.003\left(\mathrm{stat}\right)\mathrm{}\pm 0.009\left(\mathrm{syst}\right)\mathrm{}$ and ${\Gamma }_d=0.047\mathrm{}\pm 0.003\pm \mathrm{0.006.}$ The $Q^2$ dependence of the ratio $g_1{/F}_1$ was studied and found to be small for $Q^2>1\mathrm{}(\mathrm{GeV}{/c)}^2.$ 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 ${\Gamma }_p$ and ${\Gamma }_n$ below the scaling region.