Description of Relativistic Heavy--Light Quark--Antiquark Systems via Dirac Equations

Details Description of Relativistic Heavy--Light Quark--Antiquark Systems via Dirac Equations Description of Relativistic Heavy--Light Quark--Antiquark Systems via Dirac Equations

1994-01-03

arxiv.org/abs/hep-ph/9401203v1

J.Exp.Theor.Phys.78:1-14,1994; Zh.Eksp.Teor.Fiz.78:1-14,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

35 pages, preprint ITEP 83-92

Scientific paper

Starting from the QCD Lagrangian and taking into account both perturbative and nonperturbative effects, we use the method of vacuum correlators to derive the Dirac equation (rigorously for the Coulomb interaction and heuristically for the confining potential) for a system consisting of a light quark and heavy antiquark. As a result the confining potential is a Lorentz scalar, and the Coulomb part the fourth component of a 4-vector. The energy spectrum of the Dirac equation is considered for these potentials. Numerical calculations of energy eigenvalues $E=E_{n\kappa}$ are performed, and some exact solutions of the Dirac equation in the case $E=0$ are found. An effective-potential method convenient for qualitative study of the solutions of the Dirac equation is developed. The connection with experimental spectra of $D$- and $B$-mesons is briefly discussed.

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