  A renormalization group procedure for effective particles is applied to
quantum chromodynamics of one flavor of quarks with large mass m in order to
calculate light-front Hamiltonians for heavy quarkonia, H_lambda, using
perturbative expansion in the coupling constant alpha_lambda. lambda is the
renormalization group parameter with the interpretation of an inverse of the
spatial size of the color charge distribution in the effective quarks and
gluons. The eigenvalue equation for H_lambda couples quark-anti-quark states
with sectors of a larger number of constituents. The coupling to states with
more than one effective gluon, and interactions in the quark-anti-quark-gluon
sector, are removed at the price of introducing an ansatz for the gluon mass,
mu^2. The simplified equation is used to evaluate a new Hamiltonian of order
alpha_lambda that acts only in the effective quark-anti-quark sector and in the
non-relativistic limit turns out to contain the Coulomb term with Breit-Fermi
orrections and spin-independent harmonic oscillator term with frequency omega =
[(4/3)(alpha_lambda/pi)]^1/2 lambda (lambda/m)^2 (pi/1152)^1/4. The latter
originates from the hole excavated in the overlapping quark self-interaction
gluon clouds by the exchange of effective gluons between the quarks. The new
term is largely independent of the details of mu^2 and in principle can fit
into the ball park of phenomenology. The first approximation can be improved by
including more terms in H_lambda and solving the eigenvalue equations
numerically.
