Precise determination of the spin structure function ${\mathbf{g}}_1$ of the proton, deuteron and neutron

Abstract

Precise measurements of the spin structure functions of the proton $g_1^p(x,Q^2)$ and deuteron $g_1^d(x,Q^2)$ are presented over the kinematic range $0.0041\le x\le 0.9$ and $0.18$ GeV${}^2$ $\le Q^2\le 20$ GeV${}^2$. The data were collected at the HERMES experiment at DESY, in deep-inelastic scattering of 27.6 GeV longitudinally polarized positrons off longitudinally polarized hydrogen and deuterium gas targets internal to the HERA storage ring. The neutron spin structure function $g_1^n$ is extracted by combining proton and deuteron data. The integrals of $g_1^{p,d}$ at $Q^2=5$ GeV${}^2$ are evaluated over the measured $x$ range. Neglecting any possible contribution to the $g_1^d$ integral from the region $x\le 0.021$, a value of $0.330\pm 0.011(theo.)\pm 0.025(exp.)\pm 0.028$(evol.) is obtained for the flavor-singlet axial charge $a_0$ in a leading-twist NNLO analysis.