Bjorken sum rule and perturbative QCD frontier on the move

Abstract

The reasonableness of the use of perturbative QCD notions in the region close to the scale of hadronization, i.e., below $\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{GeV}$ is under study. First, the interplay between higher orders of pQCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab (JLab) data on the generalized Bjorken sum rule function ${\ensuremath{\Gamma}}_{1}^{p\ensuremath{-}n}({Q}^{2})$ at $0.1l{Q}^{2}l3\text{ }\text{ }{\mathrm{GeV}}^{2}$ is studied. It is shown that the inclusion of the higher-order pQCD corrections could be absorbed, with good numerical accuracy, by change of the normalization of the higher-twist terms. Second, to avoid the issue of unphysical singularity (Landau pole at $Q=\ensuremath{\Lambda}\ensuremath{\sim}400\text{ }\text{ }\mathrm{MeV}$), we deal with the ghost-free analytic perturbation theory (APT) that recently proved to be an intriguing candidate for a quantitative description of light quarkonia spectra within the Bethe-Salpeter approach. The values of the twist coefficients ${\ensuremath{\mu}}_{2k}$ extracted from the mentioned data by using the APT approach provide a better convergence of the higher-twist series than with the common pQCD. As the main result, a good quantitative description of the JLab data down to $Q\ensuremath{\simeq}350\text{ }\text{ }\mathrm{MeV}$ is achieved.