Boundqbar q and qqq systems with light quarks within the framework of Salpeter equations: Quarkantiquark systems
Abstract
For the boundqbar q and qqq systems with light quarks it is suggested to use the Salpeter equations, whose kernels correspond to quarkpair forces with onegluonexchange and confinement parts, both having a common colour dependence. The spin structure of the first part is taken in the standard form γ_{1μ}γ{_{1}/^{μ}}; as to the second part, its spin structure is taken in the four different forms (γ_{1μ}γ{_{1}/^{μ}}, γ{_{1}/^{0}}γ{_{1}/^{0}}, I ( I+γ{_{1}/^{0}}γ{_{1}/^{0}}/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 nonrelativistic 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 onegluonexchange part of theqbar q interaction potential. Also some mesondecay processes, such asπ to μ bar v and V(ϱ, ω, φ) → e ^{+} e ^{}, are considered for which reasonable description of the available experimental data is obtained.
 Publication:

FewBody Systems
 Pub Date:
 March 1989
 DOI:
 10.1007/BF01076280
 Bibcode:
 1989FBS.....6....1C