Analytic QCD - a short review

TL;DR

This paper reviews analytic QCD models that eliminate unphysical singularities in the coupling, enabling perturbative calculations at lower energies, and discusses their construction, strengths, weaknesses, and applications to observables.

Contribution

It provides a comprehensive overview of analytic QCD models, including new methods for constructing higher-order couplings and evaluating observables.

Findings

Several models for analytic QCD coupling are presented.

Methods for evaluating space-like and time-like observables are described.

Two models respect the ITEP Operator Product Expansion philosophy.

Abstract

Analytic versions of QCD are those whose coupling alpha_s(Q^2) does not have the unphysical Landau singularities on the space-like axis (-q^2=Q^2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q^2 < 0). Such couplings are thus suitable for application of perturbative methods down to energies of order GeV. We present a short review of the activity in the area which started with a seminal paper of Shirkov and Solovtsov ten years ago. Several models for analytic QCD coupling are presented. Strengths and weaknesses of some of these models are pointed out. Further, for such analytic couplings, constructions of the corresponding higher order analytic couplings (the analogs of the higher powers of the perturbative coupling) are outlined, and an approach based on the renormalization group considerations is singled out. Methods of evaluation of the leading-twist part of space-like observables in such analytic frameworks are described. Such methods are applicable also to the inclusive time-like observables. Two analytic models are outlined which respect the ITEP Operator Product Expansion philosophy, and thus allow for an evaluation of higher-twist contributions to observables.