High-energy scattering in the saturation regime including running coupling and rare fluctuation effects

The analytic form of the asymptotic behavior of the S matrix in the saturation regime including the running coupling is obtained. To get this result, we solve the Balitsky and Kovchegov-Weigert evolution equations in the saturation regime, which include running coupling corrections. We study also the effect of rare fluctuations on top of the running coupling. We find that the rare fluctuations are less important in the running coupling case as compared to the fixed coupling case.