The renormalization of the effective QCD Hamiltonian theory for the quark-antiquark channel is performed in terms of a renormalized or fixed-point Hamiltonian that leads to subtracted dynamical equations. The fixed-point Hamiltonian gives the renormalization conditions as well as the counterterms that render the theory finite. The approach is renormalization group invariant. The parameters of the renormalized effective QCD Hamiltonian come from the pion mass and radius for a given constituent quark mass. The $1s$ and excited $2s$ states of $ūq$ are calculated as a function of the mass of the quark $q$ being $s,$ $c,$ or $b,$ and compared to the experimental values.

• Received 21 March 2001

DOI:https://doi.org/10.1103/PhysRevD.64.054007