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Asymptotic freedom of gluons in QCD is obtained in the leading terms of theirrenormalized Hamiltonian in the Fock space, instead of considering virtualGreen's functions or scattering amplitudes. Namely, we calculate thethree-gluon interaction term in the front-form Hamiltonian for effective gluonsin the Minkowski space-time using the renormalization group procedure foreffective particles (RGPEP), with a new generator. The resulting three-gluonvertex is a function of the scale parameter, $s$, that has an interpretation ofthe size of effective gluons. The corresponding Hamiltonian running couplingconstant, $g_\lambda$, depending on the associated momentum scale $\lambda =1/s$, is calculated in the series expansion in powers of $g_0 = g_{\lambda_0}$up to the terms of third order, assuming some small value for $g_0$ at somelarge $\lambda_0$. The result exhibits the same finite sensitivity to small-$x$regularization as the one obtained in an earlier RGPEP calculation, but the newcalculation is simpler than the earlier one because of a simpler generator.This result establishes a degree of universality for pure-gauge QCD in theRGPEP.

Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons