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

QCD coupling below 1 GeV from quarkonium spectrum

In this paper we extend the work synthetically presented in Ref.[1] and give theoretical details and complete tables of numerical results. We exploit calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an ``experimental'' strong coupling \alpha_s^{exp}(Q^2) below 1 GeV by comparison with the meson spectrum. The BS potential follows from a proper ansatz on the Wilson loop to encode confinement and is the sum of a one-gluon-exchange and a confinement terms. Besides, the common perturbative strong coupling is replaced by the ghost-free expression \alpha_E(Q^2) according to the prescription of Analytic Perturbation Theory (APT). The agreement of \alpha_s^{exp}(Q^2) with the APT coupling \alpha_E(Q^2) turns out to be reasonable from 1 GeV down to the 200 MeV scale, thus confirming quantitatively the validity of the APT prescription. Below this scale, the experimental points could give a hint on the vanishing of \alpha_s(Q^2) as Q approaches zero. This infrared behaviour would be consistent with some lattice results and a ``massive'' generalization of the APT approach. As a main result, we claim that the combined BS-APT theoretical scheme provides us with a rather satisfactory correlated understanding of very high and rather low energy phenomena from few hundreds MeV to few hundreds GeV.Comment: Preliminary revision. Typos corrected, comments and references adde