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

TL;DR

This work delivers high-precision measurements of the spin structure function g1 for the proton and deuteron, enabling extraction of the neutron g1 through a combination of targets. By unfolding radiative and detector smearing and employing NLO QCD evolution, the study provides 45-bin g1 values and 19- or 15-bin representations, along with comprehensive covariance information. The deuteron data saturate at x < 0.04, allowing a robust determination of the flavor-singlet axial charge a0 and the strange-quark helicity, yielding a0 ≈ 0.33 and Δs ≈ −0.085, with Δu and Δd extracted under SU(3) symmetry assumptions. The results support a substantial quark-spin contribution to nucleon spin, while indicating the need for gluon and orbital angular momentum contributions to complete the spin sum rule, and provide a precise test of the Bjorken sum rule at NNLO in QCD.

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.

Figures (18)

• Figure 1: Schematic picture of Deep-Inelastic Scattering for one photon exchange. The kinematic variables are defined in Tab. \ref{['table:kinevar']}.
• Figure 2: Schematic view of the longitudinally polarized target. From left to right: Atomic Beam Source (ABS) containing Radio-Frequency Transitions (RFT), target chamber with cell and magnet, diagnostic system composed by Target Gas Analyzer (TGA), and Breit-Rabi Polarimeter (BRP).
• Figure 3: A schematic side view of the HERMES spectrometer.
• Figure 4: Kinematic $x-Q^2$ and $x-y$ planes covered by this analysis. The symbols represent the average values of $(x,Q^2)$ (top panel) and $(x,y)$ (bottom panel) in each bin. Subdivision of the $x$-bins along $Q^2$ is denoted by different symbols (A, B, C).
• Figure 5: Percentage of charge symmetric background in each $x-Q^2$ bin, for the proton and the deuteron targets. Subdivisions A, B, and C are those defined in Fig. \ref{['fig:xq2plane']}.