Infrared behavior of the running coupling constant and quarkonium spectrum

We study the effect of the infrared behavior of the running coupling constant on the quark-antiquark spectrum.Comment: 3 pages. 1 figure, talk given at the 5th International Conference "Quark Confinement and the Hadron Spectrum", September 10-14, 2002. Gargnano sul Garda (BS) Ital

Extracting infrared QCD coupling from meson spectrum

In the framework of the Bethe-Salpeter formalism used in previous papers to evaluate the quarkonium spectrum, here we reverse the point of view to extract an ``experimental'' running coupling alpha_s(Q^2) in the infrared (IR) region from the data. The values so obtained agree within the errors with the Shirkov-Solovtsov analytic coupling for 200 MeV <Q< 1.2 GeV, thus giving a very satisfactory unifying description of high and low energy phenomena. Below 1 GeV however alpha_s(Q^2) seems to vanish as Q to 0. The paper is based on a work in progress in collaboration with D.V.Shirkov.Comment: Talk given at 7th International Conference on Quark Confinement and the Hadron Spectrum, Azores - Portugal, 2-7 Sep 2006. To be published in AIP Conf.Pro

B_{c} meson and the light-heavy quarkonium spectrum

We compute the c \bar{b} spectrum from a first principle Salpeter equation obtained in a preceding paper. For comparison we report also the heavy-light quarkonium spectrum and the hyperfine separations previously presented only in a graphical form. Notice that all results are parameter free.Comment: 7 pages. Minor changes; references added. Accepted for publication on Phys. Rev.

Running coupling constant and masses in QCD, the meson spectrum

In line with some previous works, we study in this paper the meson spectrum in the framework of a second order quark-antiquark Bethe-Salpeter formalism which includes confinement. An analytic one loop running coupling constant alpha_s(Q), as proposed by Shirkov and Sovlovtsov, is used in the calculations. As for the quark masses, the case of a purely phenomenological running mass for the light quarks in terms of the c. m. momentum is further investigated. Alternatively a more fundamental expression m_P(Q) is introduced for light and strange quarks, combining renormalization group and analyticity requirements with an approximate solution of the Dyson-Schwinger equation. The use of such running coupling constant and masses turns out to be essential for a correct reproduction of the the light pseudoscalar mesons.Comment: 10 pages, 2 figures, conference: Quark Confinement and the Hadron Spectrum VI, Villasimius, Cagliari, Ital

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

Bound state approach to the QCD coupling at low energy scales

We exploit theoretical results on the meson spectrum within the framework of a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an ``experimental'' coupling \alpha_s^{exp}(Q^2) below 1 GeV by comparison with the data. Our results for \alpha_s^{exp}(Q^2) exhibit a good agreement with the infrared safe Analytic Perturbation Theory (APT) coupling from 1 GeV down to 200 MeV. 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 low energy phenomena.Comment: Revised version, to appear on Physical Review Letters. 7 pages, 2 figures, Revte