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

Abstract

Asymptotic freedom of gluons in pure-gauge QCD is obtained in the leading terms of their renormalized Hamiltonian in the Fock space, instead of considering virtual Green's functions or scattering amplitudes. Namely, we calculate the three-gluon interaction term in the effective front-form Hamiltonian for gluons in the Minkowski space-time using the renormalization group procedure for effective particles (RGPEP), with a new generator. The resulting three-gluon vertex is a function of the scale parameter, $s$, that has an interpretation of the size of effective gluons. The corresponding Hamiltonian running coupling constant, ${g}_{\ensuremath{\lambda}}$, depending on the associated momentum scale $\ensuremath{\lambda}=1/s$, is calculated in the series expansion in powers of ${g}_{0}={g}_{{\ensuremath{\lambda}}_{0}}$ up to the terms of third order, assuming some small value for ${g}_{0}$ at some large ${\ensuremath{\lambda}}_{0}$. The result exhibits the same finite sensitivity to small-$x$ regularization as the one obtained in an earlier RGPEP calculation, but the new calculation is simpler than the earlier one because of a simpler generator. This result establishes a degree of universality for pure-gauge QCD in the RGPEP.