Relativistic consistency of the logarithmic heavy quark model

It is shown that a non-relativistic power-law potential model for the heavy quarks in the form V(r)=Arv+V0, (A, ν>0) acquires relativistic consistency in generating Dirac bound states of $Q\bar Q$-system in agreement with the Schrodinger spectroscopy if the interaction is modelled by equally mixed scalar and vector parts as suggested by the phenomenology of fine-hyperfine splittings of heavy quarkonium systems in a non-relativistic perturbative approach.

Schrödinger vs. dirac bound state spectra of $$Q\bar Q$$ -systems and a plausible lorentz structure of the effective power-law potential-systems and a plausible lorentz structure of the effective power-law potential

The mass spectra of both light and heavy mesons are studied in the Dirac equation with an equally mixed 4-vector and scalar power-law potential model. This potential provides an excellent fit not only to the mass spectra ofp°, ϕ, Ψ and υ families but also to those ofD, F andB mesons. The light quark masses inp° and ϕ as well as in atom-like mesons are very close to the current quark masses.

Mass spectra of light and heavy mesons in the-Dirac equation with power-law potential

High‐energy asymptotic expansions of eigenenergies, wavefunctions, and Regge trajectories of the generalized even power potential V(r)=−g2∑∞j=0N2 jr2j in the Dirac equation are obtained. These general expansions are then used to obtain eigenenergy expansions and Regge trajectories for the anharmonic oscillator and Gauss potentials. Finally, the relevance of these investigations to the spectroscopy of heavy quark composites is discussed. In particular, we study the charmonium spectroscopy for an harmonic oscillator.

R. Halasa

Papers

Dirac equation with a quadratic scalar potential—are quarks confined?