  Renormalized Hamiltonians for gluons are constructed using a perturbative
boost-invariant renormalization group procedure for effective particles in
light-front QCD, including terms up to third order. The effective gluons and
their Hamiltonians depend on the renormalization group parameter lambda, which
defines the width of momentum space form factors that appear in the
renormalized Hamiltonian vertices. Third-order corrections to the three-gluon
vertex exhibit asymptotic freedom, but the rate of change of the vertex with
lambda depends in a finite way on regularization of small-x singularities. This
dependence is shown in some examples, and a class of regularizations with two
distinct scales in x is found to lead to the Hamiltonian running coupling
constant whose dependence on lambda matches the known perturbative result from
Lagrangian calculus for the dependence of gluon three-point Green's function on
the running momentum scale at large scales. In the Fock space basis of
effective gluons with small lambda, the vertex form factors suppress
interactions with large kinetic energy changes and thus remove direct couplings
of low energy constituents to high energy components in the effective bound
state dynamics. This structure is reminiscent of parton and constituent models
of hadrons.
