Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-07-24
Phys.Rev. C59 (1999) 976-985
Physics
High Energy Physics
High Energy Physics - Phenomenology
22 pages, 5 postscript figures, LaTeX-file (revtex.sty)
Scientific paper
10.1103/PhysRevC.59.976
Bound q\bar q systems are studied in the framework of different 3-dimensional relativistic equations derived from the Bethe-Salpeter equation with the instantaneous kernel in the momentum space. Except the Salpeter equation, all these equations have a correct one-body limit when one of the constituent quark masses tends to infinity. The spin structure of the confining qq interaction potential is taken in the form $x\gamma_{1}^{0}\gamma_{2}^{0}+(1-x)I_{1}I_{2}$, with $0\leq x \leq 1$. At first stage, the one-gluon-exchange potential is neglected and the confining potential is taken in the oscillator form. For the systems (u\bar s), (c\bar u), (c\bar s) and (u\bar u), (s\bar s) a comparative qualitative analysis of these equations is carried out for different values of the mixing parameter x and the confining potential strength parameter. We investigate: 1)the existence/nonexistence of stable solutions of these equations; 2) the parameter dependence of the general structure of the meson mass spectum and leptonic decay constants of pseudoscalar and vector mesons. It is demonstrated that none of the 3-dimensional equations considered in the present paper does simultaneously describe even general qualitative features of the whole mass spectrum of q\bar q systems. At the same time, these versions give an acceptable description of the meson leptonic decay characteristics.
Babutsidze T.
Kopaleishvili Teimuraz
Rusetsky A. G.
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