  Aiming at relativistic description of gluons in hadrons, the renormalization
group procedure for effective particles (RGPEP) is applied to baryons in QCD of
heavy quarks. The baryon eigenvalue problem is posed using the Fock-space
Hamiltonian operator obtained by solving the RGPEP equations up to second order
in powers of the coupling constant. The eigenstate components that contain
three quarks and two or more gluons are heuristically removed at the price of
inserting a gluon-mass term in the component with one gluon. The resulting
problem is reduced to the equivalent one for the component of three quarks and
no gluons. Each of the three quark-quark interaction terms thus obtained
consists of a spin-dependent Coulomb term and a spin-independent harmonic
oscillator term. Quark masses are chosen to fit the lightest spin-one quarkonia
masses most accurately. The resulting estimates for bbb and ccc states match
estimates obtained in lattice QCD and in quark models. Masses of ccb and bbc
states are also estimated. The corresponding wave functions are invariant with
respect to boosts. In the ccb states, charm quarks tend to form diquarks. The
accuracy of our approximate Hamiltonian can be estimated through comparison by
including components with two gluons within the same method.
