Bjorken sum rule in QCD frameworks with analytic (holomorphic) coupling

Abstract

We investigate the Bjorken polarized sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2$δ$anQCD), and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3$δ$anQCD, 4l3$δ$anQCD). These couplings do not have unphysical (Landau) singularities, and have finite values when the transferred momentum goes to zero, which allows us to explore the infrared regime. With the exception of APT, these theories at high momenta practically coincide with the underlying perturbative QCD (pQCD) in the same scheme. We apply them in order to verify the Bjorken sum rule within the range of energies available in the data collected by the experimental JLAB collaboration, i.e., $0.05 GeV^2 <Q^2< 3 GeV^2$ and compare the results with those obtained by using the perturbative QCD coupling. The results of the new frameworks with respective couplings (2$δ$ and 3$δ$) are in good agreement with the experimental data for $0.5 GeV^2<Q^2<3 GeV^2$ already when only one higher-twist term is used. In the low-$Q^2$ regime ($Q^2 \lesssim 1 GeV^2$) we use $χ$PT-motivated expression or an expression motivated by the light-front holography (LFH) QCD used earlier in the literature.