G. M. Prosperi

Bound-State Approach to the QCD Coupling Constant 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 (Q2) below 1 GeV by comparison with the data. Our results for alpha(s)exp (Q2) 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.

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 αs(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 mP(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.

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 αsexp(Q2) in the infrared (IR) region from the data. The values so obtained agree within the erros 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 αsexp(Q2) seems to vanish as Q → 0. The paper is based on a work in progress in collaboration with D. V. Shirkov.

LIGHT MESONS AND INFRARED BEHAVIOR OF THE RUNNING COUPLING CONSTANT IN QCD

A previous method for handling bound states in QCD is briefly revisited. Taking advantage of the Feynman-Schwinger representation for the iterated quark propagator in an external field, it is possible to give closed representations for certain appropriate (second order) two point and four point Green functions, H^(2)(x-y) and H^(4)(x_1,x_2,y_1,y_2), as path integrals on quark world lines. Then, starting from reasonable assumptions on the Wilson line correlators, a Bethe-Salpeter equation for H^(4) and a Dyson-Schwinger equation for H^(2) can be obtained, which are consistent with the Goldstone theorem in the chiral limit. Such equations are too complicate to be solved directly. However, a reduced Salpeter equation can be derived which is tractable and has been applied to a calculation of the meson spectrum. The results are in general good agreement with the data, but with the important exceptions of the light pseudo scalars (that are related to the breaking of the chiral symmetry). In this scenario two important improvements can be introduced: a) the fixed coupling constant can be replaced by a running coupling constant \alpha_{s}(Q^2) appropriately modified in the infrared region; b) the fixed mass in the reduced equation can be replaced for light quarks by an effective mass depending on the momentum of the particle, as suggested by the form of the DS equation. Then even the light pseudo scalar mesons can be made to agree with to their experimental value.

CONFINING BETHE–SALPETER EQUATION IN QCD

We derive a confining

INFRARED BEHAVIOR OF THE RUNNING COUPLING CONSTANT AND QUARKONIUM SPECTRUM

q \bar{q}

Quark-antiquark Bethe-Salpeter formalism, spectrum and Regge Trajectories

Bethe--Salpeter equation starting from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by

Confining Bethe-Salpeter equation from scalar QCD

{1\over m^2}

BS and DS equations in a Wilson loop context in QCD, effective mass operator, q-qbar spectrum

expansion, the corresponding Wilson loop potential is recovered, spin--dependent and velocity--dependent terms included. We also show, that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.