Dynamics of effective gluons

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 \ensuremath{\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 \ensuremath{\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 \ensuremath{\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 \ensuremath{\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.