  Light-front Hamiltonian formulation of QCD with only one flavor of quarks is
used in its simplest approximate version to calculate masses and
boost-invariant wave functions of c-anti-c or b-anti-b mesons. It is shown that
in the Hamiltonian approach in its simplest version the strong coupling
constant alpha and quark mass m (for suitable values of the renormalization
group parameter lambda that is used in the calculation), can be adjusted so
that a) masses of 12 lightest well-established b-anti-b mesons are reproduced
with accuracy better than 0.5 percent for all of them, which means 50 MeV in a
few worst cases and on the order of 10 MeV in other cases, or b) masses of 11
lightest c-anti-c mesons are reproduced with accuracy better than 3 percent for
all of them, which means better than 100 MeV in a few worst cases and on the
order of 10 MeV in the other cases, while the parameters alpha and m are near
the values expected in the cases a) and b) by analogy with other approaches. A
4th-order study in the same Hamiltonian scheme will be required to explicitly
include renormalization group running of the parameters alpha and m from the
scale set by masses of bosons W and Z down to the values of lambda that are
suitable in the bound-state calculations. In principle, one can use the
Hamiltonian approach to describe the structure, decay, production, and
scattering of heavy quarkonia in all kinds of motion, including velocities
arbitrarily close to the speed of light. This work is devoted exclusively to a
pilot study of masses of the quarkonia in the simplest version of the approach.
