Related papers: The analytical singlet $\alpha_s^4$ QCD contributi…
Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler…
Three different approaches to precisely describe the Adler function in the Euclidean regime at around $2\, \mathrm{GeVs}$ are available: dispersion relations based on the hadronic production data in $e^+e^-$ annihilation, lattice…
Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the ``generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…
We propose a conjecture about the detailed structure of the conformal symmetry breaking term in the generalized Crewther relation. We conclude that this conjecture leads to new relations between the QCD expansion coefficients of the Adler…
The present calculations in perturbative QCD reach the order $\alpha_s^4$ for several correlators calculated to five loops, and the huge computational difficulties make unlikely the full six-loop calculation in the near future. This…
It has been shown that the one-loop behavior of the axial anomaly, occurring when the axial current is appropriately normalized, leads to the cancellation of the corrections of type $C_F^N{\bar \alpha}_s^N,~~ (N\geq 1) $ in the Crewther…
Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…
Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scales, independent of the choice of intermediate renormalization scheme or other theoretical conventions. A prominent…
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 <…
The analytical $\mathcal{O}(a^4_s)$ perturbative QCD expression for the flavour non-singlet contribution to the Bjorken polarized sum rule in the rather applicable at present gauge--dependent $\rm{miniMOM}$ scheme is obtained. For the…
The conventional series in powers of the coupling in perturbative QCD have zero radius of convergence and fail to reproduce the singularity of the QCD correlators like the Adler function at $\alpha_s=0$. Using the technique of conformal…
An experimental motivated QCD analysis of the behaviour of the Adler D-function in the Euclidian region is described. It is stressed that by taking account of $b$-quark mass-dependent $\alpha_s^2$-effects one obtains better agreement…
We summarize the current status of our understanding of the structure of the perturbative QCD expressions for the QCD generalization of the Crewther relation.
In this work we consider the possibility of representing the perturbative series for renormalization group invariant quantities in QCD in the form of their decomposition in powers of the conformal anomaly $\beta(\alpha_s)/\alpha_s$ in the…
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…
Results on the resummation of non-power-series expansions of the Adler function of a scalar, $D_S$, and a vector, $D_V$, correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to…
Two-loop corrections for the <VVA> correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by…
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…
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 present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $\tau$-decay data. The determination involves the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is…