Bound$q\bar q$ andqqq systems with light quarks within the framework of Salpeter equations: Quark-antiquark systems

Abstract

For the bound$q\bar q$ andqqq systems with light quarks it is suggested to use the Salpeter equations, whose kernels correspond to quark-pair forces with one-gluon-exchange and confinement parts, both having a common colour dependence. The spin structure of the first part is taken in the standard form γ_1μγ ^μ₁ ; as to the second part, its spin structure is taken in the four different forms (γ_1μγ ^μ₁ , γ ⁰₁ γ ⁰₁ ,I (I+γ ⁰₁ γ ⁰₁ /2). A system of equations for the spinor components of the wave functions is presented. The system of equations for radial wave functions derived for the case of equal quark masses is investigated by the numerical solution method when only the confinement potential (oscillator type) is taken into account. The use of the solutions of the non-relativistic limit of these equations as a basis for expansion of the relativistic radial functions shows that for all allowed states stable solutions exist only for the second and fourth versions of the spin structure of the confinement potential. For these cases the meson spectra are calculated with allowance for the one-gluon-exchange part of the$q\bar q$ interaction potential. Also some meson-decay processes, such as$\pi \to \mu \bar v$ andV(ϱ, ω, φ) →e ⁺ e ⁻, are considered for which reasonable description of the available experimental data is obtained.