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

TL;DR

This paper assesses the Bjorken polarized sum rule using a renormalon-based approach, incorporating operator expansion terms, and fits to experimental data to extract QCD parameters, highlighting challenges due to uncertainties and low-energy limitations.

Contribution

It introduces a renormalon-motivated method to evaluate the Bjorken sum rule and incorporates higher-twist terms to fit experimental data, addressing low-Q^2 limitations.

Findings

The fit is valid for Q^2 ≥ 1.7 GeV^2 due to Landau singularities.

Large experimental uncertainties lead to significant uncertainties in the extracted parameters.

Fixing the pQCD coupling to known values allows for more constrained parameter determination.

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.