Related papers: QCD Analytic Perturbation Theory. From integer pow…
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 <…
Technical aspects of the Shirkov-Solovtsov's analytic perturbation theory (APT) are considered. We construct explicitly two sets of specific functions, ${\mathfrak{A}_n(s)}$ and ${{\cal A}_n(Q^2)}$ that determine the nonpower as ymptotic…
The removal of unphysical singularities in the perturbatively calculable part of the pion form factor--a classic example of a three-point function in QCD--is discussed. Different ``analytization'' procedures in the sense of Shirkov and…
We analyze two sets of specific functions, that/which form the basis of the nonpower asymptotic expansions both in the timelike and spacelike regions for single scale dependent QCD observables in the Shirkov--Solovtsov's Analytic…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form…
Recently, the QCD renormalization group (RG) equation at higher orders in MS-like renormalization schemes has been solved for the running coupling as a series expansion in powers of the exact 2-loop order coupling. In this work, we prove…
The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The…
I elaborate on the implementation of analyticity of hadronic quantities at the amplitude level and show that it amounts to the extension of Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer (fractional) powers of the…
The analytization procedure which allows one to remove nonphysical singularities of the QCD running coupling constant $\bar\alpha_s(q^2)$ in the infrared region is applied to standard as well as to iterative solutions of the two-loop…
The QCD analytic running coupling alpha_{an} which has no nonphysical singularities for all Q^2>0 is considered for the initial perturbation theory approximations up to four loop order. The finiteness of the analytic coupling at zero is…
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…
Fractional analytic QCD is constructed beyond leading order using the standard inverse logarithmic expansion. It is shown that, contrary to the usual QCD coupling constant, for which this expansion can be used only for large values of its…
Demanding the analyticity of hadronic observables (calculated in terms of power series of the running coupling) as a {\it whole}, we show that they are free of the Landau singularity. Employing resummation and dispersion-relation…
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of…
A simple parametrization of the QCD running coupling at low scales is introduced and used to illustrate various schemes for the estimation of non-perturbative power corrections. The `infrared matching' scheme proposed earlier gives…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
An elegant and more precise formula for the 3-loop perturbative QCD coupling is discussed. It improves the common expression (e.g., canonized by PDG) in few GeV region. On its base, we propose simple analytic Model for ghost-free QCD…
We propose a model for the QCD running coupling constant based on the Analytical Inverse QCD Coupling Constant concept with an additional regularization in the low momentum region. Analyticity in the $q^2$-complex plane, where $q$ is the…
Sudakov form factors appear ubiquitously in factorized cross sections where they allow one to resum large logarithms to all orders in perturbation theory. Their exact evaluation requires numerical integrals over anomalous dimensions, which…