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

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

Bethe-Salpeterova i Dyson-Schwingerova jednadžba i Wilsonova petlja u QCD, učinkovit operator mase i qq¯ spektar

We briefly discuss the quark-antiquark Bethe-Salpeter equation and the quark Dyson-Schwinger equation derived in preceding papers. We also consider the qq¯ quadratic mass operator M2 = (w1 + w2) 2 + U obtained by a three-dimensional reduction of the BS equation and the related approximate centre-of-mass Hamiltonian or linear-mass-operator HCM ≡ M = w1 + w2 + V + .... We review previous results on the spectrum and the Regge trajectories obtained by an approximate diagonalization of HCM and report new results similarly obtained for the original M2 . We show that in both cases we succeed to reproduce fairly well the entire meson spectrum in the cases in which the numerical calculations were actually practicable and with the exception of the light pseudoscalar states (related to the chiral symmetry problematic). A small rearrangement of the parameters and the use of a running coupling constant is necessary in the M2 case.Kratko se raspravlja Bethe-Salpeterova jednadžba za sustav kvark-antikvark i Dyson-Schwingerova jednadžba za kvarkove koje su ranije izvedene, qq¯ kvadratični operator mase M2 = (w1 + w2) 2 + U koji je izveden iz BS jednadžbe te približna Hamiltonova funkcija za centar mase odnosno linearni operator mase HCM ≡ M = w1 + w2 + V + .... Izlažu se raniji ishodi računa za spektar mezona i Reggeove putanje koji su dobiveni približnom dijagonalizacijom HCM, te navode novi ishodi koji su slično postignuti za izvorni M2 . Pokazuje se kako se u oba slučaja prilično dobro postiže cjelokupan spektar mezona za slučajeve kada su numerički računi provedivi i uz isključenje lakih pseudoskalarnih stanja (povezanih s problematikom kiralne simetrije). U slučaju M2 potrebna su mala podešavanja parametara i jedna stalnica vezanja

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