Gribov-Zwanziger confinement, high energy evolution, and large impact parameter behavior of the scattering amplitude

In this paper we derive the high energy evolution equation in the Gribov-Zwanziger approach for the confinement of quarks and gluons. We demonstrate that the new equation generates an exponential decrease of the scattering amplitude at large impact parameter and resolves the main difficulties of color glass condensate high energy effective theory. Such behavior occurs if the gluon propagator in Gribov-Zwanziger approach does not vanish at small momenta. Solving the nonlinear equation for deep inelastic scattering, we show that the suggested equation leads to a Froissart disc with radius (${R}_{F}$), which increases as ${R}_{F}\ensuremath{\propto}Y=\mathrm{ln}(1/x)$, and with a finite width for the distribution over $|b\ensuremath{-}{R}_{F}|$.