Novel Sets of Coupling Expansion Parameters for low-energy pQCD

In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant \al . However, it is known that these amplitudes are not regular functions at $\alpha=0 .$ For QCD, we propose new sets of expansion parameters {\bf w}_k(\as) that reflect singularity at \as=0 and should be used instead of powers \as^k. Their explicit form is motivated by the so called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level \as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 . They can be used for quanitative analysis of divers low-energy amplitudes. We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.Comment: 8 pages, 1 figure, submitted to Part. Nucl. Phys. Let

QCD Effective Couplings in Minkowskian and Euclidean Domains

We argue for essential upgrading of the defining equations (9.5) and (9.6) in Section 9.2 "The QCD coupling ... " of PDG review and their use for data analysis in the light of recent development of the QCD theory. Our claim is twofold. First, instead of universal expression (9.5) for QCD coupling $\bar{\alpha}_s$, one should use various ghost-free couplings $\alpha_E(Q^2), \alpha_M(s)...$ specific for a given physical representation, Euclidean, Mincowskian etc. Second, instead of power expansion (9.6) for observable, we recommend to use nonpower functional ones over particular functional sets ${{\cal A}_k(Q^2)}$, ${{\mathfrak A}_k(s)}...$ related by suitable integral transformations. We remind that use of this modified prescription results in a better correspondence of reanalyzed low energy data with the high energy ones.Comment: Contribution to proceedings of "QCD@Work2005" meeting (Bari, July 2005), 7 pages, 3 figures; v2: few other applications (with related references)adde

Renorm-group, Causality and Non-power Perturbation Expansion in QFT

The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a "$Q^2$--analytized" invariant coupling $a_{\rm an}(Q^2/\Lambda^2) \equiv {\cal A}(x)$ which, by constuction, is free of ghost singularities due to incorporating some nonperturbative structures. Meanwhile, the "analytized" perturbation expansion for an observable $F$, in contrast with the usual case, may contain specific functions ${\cal A}_n(x)= [a^n(x)]_{\rm an}$, the "n-th power of $a(x)$ analytized as a whole", instead of $({\cal A}(x))^n$. In other words, the pertubation series for $F(x)$, due to analyticity imperative, may change its form turning into an {\it asymptotic expansion \`a la Erd\'elyi over a nonpower set} $\{{\cal A}_n(x)\}$. We analyse sets of functions $\{{\cal A}_n(x)\}$ and discuss properties of non-power expansion arising with their relations to feeble loop and scheme dependence of observables. The issue of ambiguity of the invariant analytization procedure and of possible inconsistency of some of its versions with the RG structure is also discussed.Comment: 12 pages, LaTeX To appear in Teor. Mat. Fizika 119 (1999) No.