The BK equation in the conformal basis is considered and analyzed. It is shown that at high energy a factorization of the coordinate and rapidity dependence should hold. This allows to simplify significantly the from of the equation under discussion.
An analytical ansatz for the solution to the BK equation at high energies is proposed and analyzed. This analytical ansatz satisfies the initial condition at low energy and does not depend on both rapidity and the initial condition in the high energy limit. The case of the final rapidity being not too large is discussed and the properties of the transition region between small and large final rapidities have been studied.
In this paper we argue that in the kinematic range given by $ 1 ll ln(1/as^2) ll as Y ll frac{1}{as}$, we can reduce the Pomeron calculus to the exchange of non-interacting Pomerons with the renormalized 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.
