MASSES OF THE PHYSICAL MESONS FROM AN EFFECTIVE QCD HAMILTONIAN

The front form Hamiltonian for quantum chromodynamics, reduced to an e ffective Hamiltonian acting only in the <q(q)over bar> space, is solve d approximately. After coordinate transformation to usual momentum spa ce and Fourier transformation to configuration space, a second order d ifferential equation is derived. This retarded Schrodinger equation is solved by variational methods and semianalytical expressions for the masses of all 30 pseudoscalar and vector mesons are derived. In view o f the direct relation to quantum chromodynamics without a free paramet er, the agreement with experiment is remarkable, hut the approximation scheme is not adequate for the mesons with one up or down quark. The crucial point is the use of a running coupling constant alpha(s)(Q(2)) , in a manner similar, but not equal to the one of Richardson in the e qual usual-time quantization. Its value is fixed at the Z mass and the five flavor quark masses are determined by a fit to the vector meson quarkonia.