Spectroscopy of pseudoscalar and vector mesons and their electroweak decays

Proceeding from the effective action of QCD for bilocal meson fields the formula for the action describing the spectroscopy of mesons and their electroweak decays is obtained. The numerical solutions of the Salpeter equation (SE) for the qq-bound state and the Schwinger-Dyson equation (SDE) for the quark phase function are obtained with potential as sum of the oscillator and Coulomb terms. It is shown that for the oscillator potential and current quark mass m0 < 300 MeV the nontrivial solution of the SDE, which describes the spontaneous breakdown of the chiral symmetry effects and arising of the constituent quark mass, exists. Using the potential mentioned above the spectroscopy of pseudoscalar mesons is described and is shown that one reproduces the experimental data on a qualitative level. However, the values obtained for leptonic decay constant of charged pion π and width of the two-photon annihilation of neutral pion Γ(π0 → γγ) are 3-4 times smaller than their experimentations. This discrepancy was not removed even choosing other shapes of the potential. In order to resolve this problem the modification of the SDE, which consists in introducing the additional terms that do not change asymptotical properties of solutions of this equation is proposed. Using such modification both constant fπ and Γ(π0 → γγ) are reproduced on a good quantitative level. The new SE for vector mesons is proposed and its solution with potential mentioned above gives the mass spectra of these mesons. Considering the τ → ρν decay the representation for leptonic decay constant of ρ meson fπ, which expresses via solutions of the SDE and the proposed SE with a given potential is obtained. It is shown that the proposed SE allows to describe both the spectroscopy of vector mesons and their leptonic decay constants on a satisfactory level in comparison with the experimental values. (author)