# Bjorken polarized sum rule and infrared-safe QCD couplings

## TL;DR

This paper compares different QCD models, including perturbative and analytic versions, in fitting polarized Bjorken sum rule data, highlighting the advantages of infrared-safe couplings without Landau singularities.

## Contribution

It introduces a comprehensive comparison of four QCD variants, demonstrating improved fits with analytic QCD models that avoid Landau singularities at low Q^2.

## Key findings

- 2δ and 3δ analytic QCD models provide the best fit results
- Infrared-safe QCD couplings improve the fitting procedure
- Fitting quality decreases when elastic contributions are included in total BSR

## Abstract

Experimental data obtained for the polarized Bjorken sum rule (BSR) $\Gamma_1^{p-n}(Q^2)$ are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered: perturbative QCD (pQCD) in the MSbar scheme, Analytic Perturbation Theory (APT), and 2$\delta$ and 3$\delta$ analytic QCD versions. In contrast to pQCD, these QCD variants do not have Landau singularities at low positive $Q^2$, which facilitates the fitting procedure significantly. The fitting procedure is applied first to the experimental data of the inelastic part of BSR, and the known elastic contributions are added after the fitting. In general, when 2$\delta$ and 3$\delta$ QCD coupling is used the fitted curves give the best results, within the $Q^2$-range of the fit as well as in extended $Q^2$-intervals. When the fitting procedure is applied to the total BSR, i.e., to the sum of the experimental data and the elastic contribution, the quality of the results deteriorates significantly.