Unitarization of Gluon Distribution in the Doubly Logarithmic Regime at High Density

We analyze the general nonlinear evolution equations for multi gluon correlators derived in hep-ph/9709432 by restricting ourselves to a double logarithmic region. In this region our evolution equation becomes local in transverse momentum space and amenable to simple analysis. It provides a complete nonlinear generalization of the GLR equation. We find that the full double log evolution at high density becomes strikingly different from its linear doubly logarithmic DGLAP counterpart. An effective mass is induced by the nonlinear corrections which at high densities slows down the evolution considerably. We show that at small values of impact parameter the gluonic density grows as a logarithm of energy. At higher values of impact parameter the growth is faster, since the density of gluons is lower and nonlinearities are less important.