Flow equations in the light-front QCD: mass gap and confinement

Abstract

The light-front QCD is studied using the method of flow equations. Solving the light-front gluon gap equation, the effective gluon mass is generated dynamically. The effective interaction between static quark and antiquark, generated through elimination of the quark-gluon minimal coupling by flow equations, has the Coulomb, $1/q^2$, and confining, $1/q^4$, singular behavior. Elimination of the quark-gluon coupling at small gluon momenta is governed by the cutoff dependent, dynamical gluon mass, which makes this elimination possible and provides such an enhancement at $q\sim 0$. The cutoff, which regulates small light-front $x$ divergences, sets up a scale for the dynamical gluon mass and the string tension in the $q\bar{q}$-potential. The mechanism of confimenemet in the light-front frame is suggested, based on the singular nature of the light-front gauge along the light-front $x$-axis.