Summing pomeron loops in the dipole approach

In this paper, we argue that in the kinematic range given by 1 ≪ ln (1 / α_S²) ≪ α_S Y ≪ frac(1, α_S), we can reduce the pomeron calculus to the exchange of non-interacting pomerons, with the renormalised amplitude of their interaction with the target. Therefore, the summation of the pomeron loops can be performed using the improved Mueller, Patel, Salam and Iancu approximation, and this leads to the geometrical scaling solution. This solution, is found for the simplified BFKL kernel. We reproduce the findings of Hatta and Mueller, that there are overlapping singularities. We suggest a way of dealing with these singularities.