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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)

Abstract

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.

Keywords

Rest Masse Mass Splitting Nonrelativistic Limit Heavy Quarkonia Spinless Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    I.T. Todorov: Phys. Rev. D3 2351, (1971); V.A. Rizov, H. Sazdjian, I.T. Todorov: Ann. Phys. (NY) 165, 59 (1985)ADSGoogle Scholar
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    M.G. Olsson, K.J. Miller: Phys. Rev. D28, 674 (1983); R.W. Childers: Phys. Rev. D36, 606, 3813 (1987); W. Lucha, F.F. Schöberl: Die Starke Wechselwirkung. Eine Einführung in nichtrelativistische Potentialmodelle. Mannheim: Bibliographisches Institut & F. A. Brockhaus 1989ADSGoogle Scholar
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    M. Hirano, K. Iwata, K. Kato, T. Murota: Prog. Theor. Phys. 67, 1251 (1982); D.D. Brayshaw: Phys. Rev. D36, 1465 (1987); S.N. Grudtsin: Potential Models and Heavy Quarkonia Spectroscopy. Preprint IHEP 88-38. Serpukhov 1988ADSCrossRefGoogle Scholar
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    E.B. Berdnikov, G.P. Pron’ko: Sov. J. Nucl. Phys. 54, 763 (1991); E.B. Berdnikov, G.G. Nanobashvili, G.P. Pron’ko: ibid 55, 203 (1992)Google Scholar

Copyright information

© Springer-Verlag/Wien 2003

Authors and Affiliations

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

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