Flow equations in the light-front QCD

Abstract

Flow equations method of continuous unitary transformations is used to eliminate the minimal quark-gluon interaction in the light-front quantized QCD Hamiltonian. The coupled differential equations in the two lowest Fock sectors correspond to the renormalization of the light-front gluon mass and the generation of effective quark-antiquark interaction. The influence of the renormalization of the gluon effective mass on the elimination of the quark-gluon coupling and the induced quark-antiquark interaction is taken into account. Namely, the original gauge field coupling can be completely eliminated, even when the states connected by this interaction are degenerate. Furthermore, even in the case where effective interaction, obtained within perturbative schemes (bound state perturbation theory or perturbative similarity approach), is not defined, we obtain more singular behavior $1/q^4$ at small gluon momenta. This is due to asymptotic behavior of the effective gluon mass at small cutoffs. By discussing the consequences of this asymptotic behavior, it seems that our approach is superior to perturbation theory and to perturbative similarity approach.