Related papers: Ten years of the Analytic Perturbation Theory in Q…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
A brief review of the recently developed model for the QCD analytic invariant charge is presented. The main idea of this approach is invoking the analyticity condition into the framework of the renormalization group method. More precisely,…
Analytic structure in the strong coupling constant that emerges for some observables in QCD after duality averaging of renormalization group improved amplitudes is discussed. It is shown that perturbation theory calculations are justified…
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…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We investigate a new ``renormalization invariant analytic formulation'' of calculations in quantum chromodynamics, where the renormalization group summation is correlated with the analyticity with respect to the square of the transferred…
This paper gives an overview of recently developed model for the QCD analytic invariant charge. Its underlying idea is to bring the analyticity condition, which follows from the general principles of local Quantum Field Theory, in…
In the framework of the analytic approach to Quantum Chromodynamics a new model for the strong running coupling has recently been developed. Its underlying idea is to impose the analyticity requirement on the perturbative expansion of the…
We propose a new generalized version of the QCD Analytic Perturbation Theory of Shirkov and Solovtsov for the computation of higher-order corrections in inclusive and exclusive processes. We construct non-power series expansions for the…
Solving the QCD renormalization group equation at the 2-loop and 3-loop orders we obtain explicit expressions for the coupling as a function of the scale in terms of the Lambert W function. We study the nature of the ``Landau…
Starting from the divergence pattern of perturbative quantum chromodynamics, we propose a novel, non-power series replacing the standard expansion in powers of the renormalized coupling constant $a$. The coefficients of the new expansion…
The connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions is studied. Our basic tool is the "double spectral representation", similar to definition of Adler function,…
The renormalization group applied to perturbation theory is ordinarily used to define the running coupling constant in the spacelike region. However, to describe processes with timelike momenta transfers, it is important to have a…
Using renormalization-group methods, differential equations can be obtained for the all-orders summation of leading and subsequent non-leading logarithmic corrections to QCD perturbative series for a number of processes and correlation…
The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\alpha$, in Quantum Theory. We start with outlining a…
We briefly summarize some recent theoretical developments in perturbative QCD, emphasizing new ideas which have led to widening the domain of applicability of perturbation theory. In particular, it is now possible to calculate efficiently…
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…
In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions.…
Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = sigma(e^+ e^- --> hadrons)/sigma(e^+ e^- --> mu^+ mu^-), as obtained from the…
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD -- ghost singularities and…