Fractional Analytic QCD: The Recent Results

In this work, we present an overview of fractional analytic QCD in the spacelike (Euclidean) and timelike regions, which significantly improves the coupling constant in perturbative QCD. The obtained results are applied to the description of the Higgs boson decay into a bottom-antibottom pair and the polarized Bjorken sum rule. For the latter, an additional modification is proposed to combine the fitting curve with the condition for photoproduction.We found good agreement between the experimental data obtained for the polarized Bjorken sum rule and the predictions of analytic QCD, as well as a strong difference between these data and the results obtained in the framework of perturbative QCD. To satisfy the limit of photoproduction and take into account GerasimovDrell-Hearn and Burkhardt-Cottingham sum rules, we develope new representation of the perturbative part of the polarized Bjorken sum rule. We present an overview of fractional analytic QCD and its application for Higgs-boson decay into a bottom-antibottom pair and the description of the polarized Bjorken sum rule. The results shown here have been recently obtained in Refs. [18,19,21,22]. This study is dedicated to the description of the polarized Bjorken sum rule, based on recently derived formulas within the analytic QCD approach. To accommodate the photoproduction limit and incorporate the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules, we develop a new representation for the twist-2 part of the Bjorken sum rule. The derived results were applied for processing of experimental data. We observed a good agreement between the experimental data and the predictions from analytic QCD. In contrast, there is a significant discrepancy between these data and the fitting curves within the standard perturbative approach.