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We give a short review of our recent analysis [1] of the deep inelastic scattering data (provided by BCDMS, SLAC, NMC) on F2 structure function in the non-singlet approximation with up to next-to-next-to-leading-order accuracy and analytic…
An analytic ghost-free model for the QCD running coupling $\alpha(Q^2)$ is proposed. It is constructed from a more general approach we developed particularly for investigating physical observables of the type $F(Q^2)$ in regions that are…
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…
Methods described in the literature for the computation of the QCD running coupling are essentially all defined with respect to the renormalization group equations and these equations are associated with the method of renormalization for…
Part I is devoted to the extraction of the QCD coupling from a bound state approach at low energy scales, where unphysical singularities make the RG-improved pQCD useless. Theoretical results on the meson spectrum based on a Bethe-Salpeter…
Perturbative QCD in mass independent schemes leads in general to running coupling $a(Q^2)$ which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta $|Q^2| \lesssim 1 \ {\rm GeV}^2$. Such (Landau) singularities are…
In contrast to perturbative QCD, the analytic QCD models have running coupling whose analytic properties correctly mirror those of spacelike observables. The discontinuity (spectral) function of such running coupling is expected to agree…
We use the BLM procedure to eliminate the renormalization scale ambiguity in the evolution equation for the non-singlet deep-inelastic structure function $F_2^{\text NS}(x,Q).$ The scale of the QCD coupling in the $\overline{\text{MS}}$…
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…
The mathematical properties of the new analytic running coupling (NARC) in QCD are investigated. This running coupling naturally arises under ``analytization'' of the renormalization group equation. One of the crucial points in our…
Quark-hadron duality is studied in a systematic way for polarized and unpolarized structure functions, by taking into account all the available data in the resonance region. In both cases, a precise perturbative QCD based analysis of the…
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…
We provide a Mathematica package that evaluates the QCD analytic couplings (in the Euclidean domain) $\mathcal{A}_{\nu}(Q^2)$, which are analytic analogs of the powers $a(Q^2)^{\nu}$ of the underlying perturbative QCD (pQCD) coupling…
We present an analysis of the role of the running coupling constant at the intersection of perturbative and nonperturbative QCD in the context of the quark-hadron duality \`a la Bloom-Gilman. Our framework will be the unpolarized structure…
We construct models of analytic QCD (i.e.,with the running coupling parameter free of Landau singularities) which address several problems encountered in previous analytic QCD models, among them their incompatibility with the ITEP-OPE…
In this contribution to the proceedings, we analyze the transition from perturbative and non- perturbative QCD embedded in the coupling constant. In the study of quark-hadron duality, we suggest that the realization of the latter is related…
The normalization of the gluon condensate and of renormalon-related power corrections in QCD is computed under the assumption that their ``perturbative'' part dominates over any eventual extra contribution from the non-trivial vacuum. The…
We consider computational problems in the framework of nonpower Analityc Perturbation Theory and Fractional Analytic Perturbation Theory that are the generalization of the standard QCD perturbation theory. The singularity-free, finite…
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 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…