The Spin Structure Function $g_1^{\rm p}$ of the Proton and a Test of the Bjorken Sum Rule

TL;DR

This paper presents new measurements of the proton spin structure function $g_1^{\rm p}$, tests the Bjorken sum rule, and refines the quark spin contribution to the nucleon spin using COMPASS data and NLO QCD fits.

Contribution

It provides improved experimental data for $g_1^{\rm p}$, a refined determination of the quark spin contribution $\Delta \Sigma$, and a validation of the Bjorken sum rule within experimental uncertainties.

Findings

Enhanced precision of $g_1^{\rm p}$ at low $x$ by a factor of two.

Determined $\Delta \Sigma$ to be between 0.26 and 0.36.

Validated the Bjorken sum rule with about 9 ext{%} accuracy.

Abstract

New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\rm p}(x)$ by about a factor of two in the region $x\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\Delta \Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\rm p}$. The uncertainty of $\Delta \Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\rm A}/g_{\rm V}| = 1.22 \pm 0.05~({\rm stat.}) \pm 0.10~({\rm syst.})$, which validates the sum rule to an accuracy of about 9\%.