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

Abstract

New results for the double spin asymmetry $A_1^{\mathrm{p}}$ and the proton longitudinal spin structure function $g_1^{\mathrm{p}}$ 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 $g_1^{\mathrm{p}}(x)$ 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, $\hat{I}”\hat{I}\pounds$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\mathrm{p}}$. The uncertainty of $\hat{I}”\hat{I}\pounds$ 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 $g_1^{\mathrm{NS}}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\mathrm{A}}/g_{\mathrm{V}}|=1.22\pm 0.05(stat.)\pm 0.10(syst.)$, which validates the sum rule to an accuracy of about 9\%.

19 pages, 8 figures and tables