Analytic Approach to Perturbative QCD

TL;DR

This paper develops an analytic framework for perturbative QCD using Lambert W functions, exploring the coupling's analyticity, nonperturbative ambiguities, and solutions for the gluon propagator.

Contribution

It introduces a novel analytic approach to QCD coupling and propagator calculations using Lambert W functions, addressing nonperturbative ambiguities.

Findings

The two-loop QCD coupling is expressed via Lambert W function.

Analytic structure of the coupling in the complex plane is characterized.

Multiple analytic solutions for the gluon propagator are constructed.

Abstract

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.