Global Fractional Analytic Perturbation Theory in QCD with Selected Applications

TL;DR

This paper extends Fractional Analytic Perturbation Theory (FAPT) for QCD to include heavy-quark thresholds, providing a unified approach for both Euclidean and Minkowski regions and applying it to phenomenological processes.

Contribution

The paper develops a global version of FAPT that accounts for heavy-quark thresholds and applies it to relevant QCD processes and series summation.

Findings

Constructed a global FAPT incorporating heavy-quark thresholds.

Applied FAPT to e+e- annihilation and pion form factor.

Demonstrated FAPT's effectiveness in QCD phenomenology.

Abstract

We give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of squared momentum transfer q^2, which takes into account heavy-quark thresholds. The original analytic approach to QCD, initiated by Jones, Solovtsov and Shirkov, is shortly summarized. We also shortly consider the basic aspects of FAPT and then concentrate on the accounting for the heavy-quark thresholds problem and the construction of global version of FAPT. We discuss what one should use as an analytic coupling in the timelike region q^2=s>0 for the e^{+}e^{-}-annihilation and the pion form factor, and consider applications to phenomenologically relevant processes (the factorizable part of the pion form factor and the Higgs boson decay into a b\bar{b} pair), as well as to the summation of perturbative series.