Flow Equations in the Light-front Qcd: Mass Gap and Confinement

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 ∼ 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 ¯ 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.