Determination of the Bjorken Sum and Strong Coupling from Polarized Structure Functions
Guido Altarelli, Richard D. Ball, Stefano Forte, Giovanni Ridolfi
TL;DR
The study addresses the problem of testing the Bjorken sum rule and determining the strong coupling constant from polarized structure-function data by performing a comprehensive NLO QCD analysis of $g_1(x,Q^2)$ across proton, neutron, and deuteron targets. It models polarized parton densities with several input forms at a low scale $Q_0^2=1$ GeV$^2$, evolves them to the measured kinematic region, and extracts first-moment observables such as the isotriplet axial charge $g_A$ and singlet moments, while carefully treating small-$x$ extrapolation. The main findings are that $g_A=1.19\pm0.09$, consistent with the Bjorken sum rule at the ~8% level, and that $\alpha_s(m_Z)=0.120^{+0.010}_{-0.008}$, dominated by scaling violations rather than the Bjorken integral alone; the data also indicate a sizeable positive gluon polarization, with singlet moments suggesting a partial reconciliation of the spin sum rule. The analysis highlights that uncertainties in the small-$x$ region and higher-order corrections presently limit the precision of first-moment extractions, pointing to improved polarized DIS data at low $x$ and high $Q^2$ as the path to tighter constraints on nucleon spin structure and $ abla_s$.
Abstract
We present a NLO perturbative analysis of all available data on the polarized structure function g_1(x,Q^2) with the aim of making a quantitative test of the validity of the Bjorken sum rule, of measuring α_s, and of deriving helicity fractions. We take particular care over the small x extrapolation, since it is now known that Regge behaviour is unreliable at perturbative scales. For fixed α_s we find that if all the most recent data are included g_A=1.18\pm0.09, confirming the Bjorken sum rule at the 8% level. We further show that the value of α_s is now reasonably well constrained by scaling violations in the structure function data, despite the fact that it cannot yet be reliably fixed by the value of the Bjorken sum: our final result is α_s(m_Z) = 0.120+0.010-0.008. We also confirm earlier indications of a sizeable positive gluon polarization in the nucleon.