MASS SPECTRA OF RADIALLY AND ORBITALLY EXCITED STATES OF MESONS

Meson mass spectra, evaluated in the framework of the relativistic model of quasi-independent quarks, are presented. Mass values are obtained with the help of numerical calculations based on the Dirac equation and by phenomenological mass formulae. The Dirac equation involves the potential, which is sum of the vector quasi-Coulombic potential and the scalar linear rising confinement potential. The phenomenological mass formulae are applied to excited meson states consisting of u , d quarks and antiquarks with isotopical spin I = 1. A comparison of the evaluated mass spectra with existing data is performed. Problems of identification of some meson states in vector and scalar channels are discussed. It is known that the calculation of hadron mass spectra on the level of experimental data precision [1] still remains among the unsolved QCD problems due to some technical and conceptual difficulties, which are related mainly with the nonperturbative effects, such as confinement and spontaneous chiral symmetry breaking. Nowadays hadron characteristics calculations are frequently carried out with the help of phenomenological models. Among phenomenological models the potential quark models are the simplest ones, they make it possible to represent the different stages of calculations in terms of commonly used physical quantities. Although these models are suitable rather well for the heavy quark hadrons treating of hadrons containing the light quarks is more complicated task, which demands relativistic and nonpotential effects to be taken into account [2, 3, 4]. The relativistic model of quasi-independent quarks is applicable to the description of properties of light and heavy hadrons [5, 6, 7, 8]. Below we present the results of calculations in the framework of this model [8, 9, 10] of mass spectra of quarkonium type mesons, which are orbitally and radially excited states. We compare results obtained with data, make predictions for mass values of unobserved yet meson states and discuss possible structures of some mesons in scalar and vector channels. According to the main statement of the independent-quark model a hadron is considered as a system composed of a few non-interacting with each other directly valency constituents (quarks, diquarks and constituent gluons) with the coordinates ri, i = 1, ..., N, which moving in some mean colour singlet confining field. It is assumed that the field is spherically symmetric and its motion in space is determined by motion of its center with the coordinate r0. We treat the mean field as a quasi-classical object possessing some energy ǫ0. Meantime each of N constituents interacting with the mean field gets the state with a definite value of its energy ǫi, which can be determinated after solving of the model equation. We choose the Dirac equation as the model equation for quarks (the Klein-Gordon equation for diquarks and constituent gluons): q λi + m 2 ψi(ri) = [(�ipi) + βi(mi + V0) + V1] ψi(ri), (1) with Ei(n r , ji) = p λi + m 2 , i = 1,2, V0(r) = σr/2 and V1(r) = −2αs/3r, where the model parameters σ and αs have meanings of the string tension and the strong coupling constant at small distances, correspondingly. In order to exclude superfluous meson states, the following selection rules for n 2S+1 LJ -states with quark masses m1, m2 and quantum numbers n r , j1, n r , j2 are used n r = n r = n − 1, j1 = j2 = J + 1/2, if J = L + S, j1 = j2 + 1 = J + 3/2, if J 6 L + S, m1 ≤ m2,