The Spin-dependent Structure Function of the Proton g_1^p and a Test of the Bjorken Sum Rule

Abstract

The inclusive double-spin asymmetry, A_1^p, has been measured at COMPASS in deepinelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range Q2 > 1 (GeV/c)^2, 0.004 < x < 0.7 and improve the statistical precision of g_1^p(x) by a factor of two in the region x < 0.02. The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function g_1^NS(x,Q2). The isovector quark density, Delta_q_3(x,Q2), is evaluated from a NLO QCD fit of g_1^NS. The first moment of Delta_q3 is in good agreement with the value predicted by the Bjorken sum rule and corresponds to a ratio of the axial and vector coupling constants g_A/g_V = 1.28+-0.07(stat)+-0.10(syst).

Figures (5)

• Figure 1: The dilution factor $f$ of the NH$_3$ polarised target as a function of $x$ for inclusive and hadron triggerssmc. The values of $f(x)$ are averaged over the $Q^2$ range of the corresponding triggers.
• Figure 2: The asymmetry $A_1^p(x)$ as measured by COMPASS and previous results from EMC emc, SMC smc, HERMES semiinc4, SLAC E143 e143, E155 e155 and CLAS CLAS at $Q^2>1\,({\rm GeV}/c)^2$. The cut $W>2.5$ GeV has been applied to select DIS events in the CLAS data. Only statistical errors are shown with the data points. The band at the bottom shows the estimated size of the systematic errors for the COMPASS data.
• Figure 3: Values of $A_1^p$ as a function of $Q^2$ in intervals of $x$. The errors are statistical only. The solid lines show the results of fits to a constant.
• Figure 4: The spin structure function $g_1^p(x,Q^2)$ vs. $x$ as measured by COMPASS at the $Q^2$ of each measured point. Previous results from SMC smc are shown for comparison. The errors are statistical only.
• Figure 5: Left: Values of $g_1^{NS}(x)$ at $Q^2=3\,({\rm GeV}/c)^2$, derived from the COMPASS measurements of $A_1^p$ and $A_1^d$ and result of a three parameter QCD fit at NLO. The errors are statistical only. Right: $\int_{x_{min}}^1 g_1^{NS} dx$ as a function of $x_{min}$ as obtained from the COMPASS data points. The open circle at $x=0.7$ is obtained from the fit. The arrow on the left side shows the value expected for the full range $0 < x < 1$ with $|g_A/g_V| = 1.269$amsler.