saturate, but they seem to require that there be such saturation phenomena. So saturation was assumed rather than found in these approaches. The matching of this statistical picture with field-theory calculations has been attempted [@Iancu:2004iy], and has led to the statement that the Balitsky-Jalilian Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (B-JIMWLK) equations [@Balitsky:1995ub; @JIMWLK; @Weigert:2005us] were incomplete, and that they had to be supplemented with new terms. The problem was identified as follows: The Balitsky equations only contain splittings of partons, while mergings are needed in order to achieve saturation. The hope that merging rates could be obtained by boosting splitting vertices was turned down by the finding that this procedure would lead to negative probabilities [@MSW; @IST], which is at least inconvenient in practice [@MMX], if not completely meaningless.

In this paper, we go back to the original formulation of saturation by Mueller in the context of the color dipole model [@M1; @M2; @M3], which was in fact based on the assumption that saturation of the parton densities is equivalent to unitarization of the scattering amplitudes through multiple exchanges between linearly-evolved Fock states of the incoming particles (if the rapidity is not too high). Analytical calculations have been achieved within similar approximations (see Refs. 