Precision Measurement of the Deuteron Spin Structure Function $g_1^{\mathit{d}}$

We report on a high-statistics measurement of the deuteron spin structure function $g_1^d$ at a beam energy of 29 GeV in the kinematic range $0.029<x<\mathrm{}0.8\mathrm{}$ and $1<\mathrm{}{Q}^2<10\mathrm{}$ (GeV $/c$${)}^2$. The integral ${\gamma }_1^d=\int 1^{}{g}_1^d\mathrm{dx}$ evaluated at fixed $Q^2=3\mathrm{}$ (GeV $/c$${)}^2$ gives $0.042\pm 0.003\left(\mathrm{stat}\right)\pm 0.004\left(\mathrm{syst}\right)$. Combining this result with our earlier measurement of $g_1^p$, we find ${\gamma }_1^p-{\gamma }_1^n=0.163\mathrm{}\pm 0.010\left(\mathrm{stat}\right)\pm 0.016\left(\mathrm{syst}\right)$, which agrees with the prediction of the Bjorken sum rule with $O\left({\alpha }_s^3\right)$ corrections, ${\gamma }_1^p-{\gamma }_1^n=0.171\mathrm{}\pm 0.008$. We find the quark contribution to the proton helicity to be $\Delta q=0.30\mathrm{}\pm 0.06$.