Precise determination of the spin structure function $\mathbf{g_1}$ of the proton, deuteron and neutron

TL;DR

This paper presents precise measurements of the spin structure functions of the proton, deuteron, and neutron over a broad kinematic range, providing insights into the nucleon spin composition through deep-inelastic scattering data.

Contribution

It offers the first precise determination of the spin structure functions $g_1^p$, $g_1^d$, and $g_1^n$ over a wide kinematic range, including the extraction of the flavor-singlet axial charge $a_0$ using NNLO analysis.

Findings

Measured $g_1^p$ and $g_1^d$ over $0.0041 \, \leq x \leq 0.9$ and $0.18$ GeV$^2$ $\leq Q^2 \leq 20$ GeV$^2$.

Extracted $g_1^n$ from proton and deuteron data.

Determined $a_0 = 0.330 \pm 0.011\mathrm{(theo.)} \pm 0.025\mathrm{(exp.)} \pm 0.028$.

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 $0.0041 \leq x \leq 0.9$ and $0.18 $ GeV$^2$ $\leq Q^2 \leq 20$ 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 $x \leq 0.021$, a value of $0.330 \pm 0.011\mathrm{(theo.)}\pm0.025\mathrm{(exp.)}\pm 0.028$(evol.) is obtained for the flavor-singlet axial charge $a_0$ in a leading-twist NNLO analysis.