Evaluation of Bjorken polarised sum rule with a renormalon-motivated approach

Abstract

We use the known renormalon structure of Bjorken polarised sum rule (BSR) ${\overline \Gamma}_1^{p-n}(Q^2)$ to evaluate the leading-twist part of that quantity. In addition, we include $D=2$ and $D=4$ Operator Product Expansion (OPE) terms and fit this expression to available experimental data for inelastic BSR. Since we use perturbative QCD (pQCD) coupling, which fails at low squared spacelike momenta $Q^2 \lesssim 1 \ {\rm GeV}^2$ due to Landau singularities, the fit is performed for $Q^2 \geq Q^2_{\rm min}$ where $Q^2_{\rm min} \approx (1.7 \pm 0.3) \ {\rm GeV}^2$. Due to large BSR experimental uncertainties, the extracted value of the pQCD coupling has very large uncertainties, especially when $Q^2_{\rm min}$ is varied. However, when we fix the pQCD coupling to the known world average values, the $D=2$ and $D=4$ residue parameters can be determined within large but reasonable uncertainties.