VARIATIONAL TAMM-DANCOFF TREATMENT OF QUANTUM CHROMODYNAMICS - THE HEAVY MESONS IN THE VALENCE QUARK APPROXIMATION

Singular integral equations for meson spectra are obtained by making a Fock space expansion of the quantum chromodynamics (QCD) mass eigenst ate followed with a partial wave decomposition. The expansions are tru ncated and approximate equations for the mass eigenvalues and eigenvec tors are derived variationally. Using values for the QCD coupling cons tant and the quark rest masses obtained from a relativistic two-consti tuent quark model as starting values, the resulting singular integral equations for the heavy mesons are then solved by iteration to converg ence in momentum space using an expansion in cubic B splines. In these initial variational calculations we restrict ourselves to configurati ons having a maximum of one q ($) over bar qpair and 20 gluons. Howeve r, we do not introduce any phenomenological confinement interaction. N evertheless these variational results compare favorably with the resul ts of the phenomenological two-constituent quark model and with experi ment. Remarkably, we find no evidence for any continuum. There is no p arameter adjustment in these initial variational calculations. In a se cond set of variational calculations the quark masses and QCD coupling constant are determined by a fit to the heavy meson spectrum again wi thout employing a phenomenological confining potential. We then obtain an improved description of the heavy meson spectrum compared with exp eriment.