We investigate the polarized Bjorken sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2[Formula: see text]anQCD) and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3[Formula: see text]anQCD, 4l3[Formula: see text]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. [Formula: see text] and compare the results with those obtained by using the perturbative QCD coupling. The results of the new frameworks with respective couplings (2[Formula: see text] and 3[Formula: see text]) are in good agreement with the experimental data for [Formula: see text] already when only one higher-twist term is used. In the low-[Formula: see text] regime [Formula: see text], we use [Formula: see text]PT-motivated expression or an expression motivated by the light-front holography (LFH) QCD used earlier in the literature.
The Bjorken sum rule in the analytic approach to perturbative QCD