Heuristic Model of Two-Quark Relativistic System with Scalar-Vector Interaction

  • A. Duviryak
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 14)


I. Todorov has observed that the Klein-Gordon equation
$$\left \{ \textup{p}^{2}+\left [ m+V_{s}\left ( r \right ) \right]^{2}-\left [ E-V_{\textup{v}}\left ( r \right ) \right ]^{2}\right \}\mathit{\Psi}\left ( r \right)=0$$
(here p = − i ) can be transformed, by means of the substitution
$$En \to E_{M}=\frac{M^{2}-m_{1}^{2}-m_{2}^{2}}{2M},\ mn \to m_{M}=\frac{m_{1}m_{2}}{M}$$
, into the quasipotential equation describing the scalar V s (r) and vector V v(r) interactions of two spinless particles of the rest masses m a (a = 1, 2) [1]. In the case of Coulomb potentials this equation reproduces the QFT spectrum of the total mass M of the system up to α 4-terms of coupling constant expansion.


Rest Masse Mass Splitting Nonrelativistic Limit Heavy Quarkonia Spinless Particle 
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  1. 1.
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Copyright information

© Springer-Verlag/Wien 2003

Authors and Affiliations

  • A. Duviryak
    • 1
  1. 1.Institute for Condensed Matter PhysicsLvivUkraine

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