Unitarization of gluon distribution in the doubly logarithmic regime at high density

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Abstract
We analyze the general nonlinear evolution equations for multigluon correlators derived in a previous paper 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 Gribov-Levin-Ryskin equation. We find that the full double log evolution at high density becomes strikingly different from its linear doubly logarithmic Dokshitzer-Gribov-Lipatov-Alterelli-Parisi 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.