Large impact parameter behavior in the CGC/saturation approach: A new nonlinear equation

In this paper we propose a solution to the long standing problem present in the color glass condensate/saturation approach: i.e., the powerlike fall off of the scattering amplitudes at large b . We propose a new nonlinear equation, which takes into account random walks both in transverse momenta of the produced gluons, and in their impact parameter. We demonstrate, that this equation is in accord with previous attempts to include diffusion in impact parameters in the Balitsky-Fadin-Kuraev-Lipatov evolution equation. We show in the paper, that the solution to a new equation results in the exponential decrease of the scattering amplitude at large impact parameter, and in the restoration of the Froissart theorem.