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 $Q^2\lesssim 1{\mathrm{GeV}}^2$ due to Landau singularities, the fit is performed for $Q^2\ge Q_{\min }^2$ where $Q_{\min }^2\approx (1.7\pm 0.3){\mathrm{GeV}}^2$. Due to large BSR experimental uncertainties, the extracted value of the pQCD coupling has very large uncertainties, especially when $Q_{\min }^2$ 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.

Comments: 10 pages, 3 figures; v2: minor changes and references added; v3: improved text, version as published in Physics Letters B