In this paper, we use the re-summation procedure, suggested in Refs.\cite{DIMST,SALAM,SALAM1,SALAM2}, to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce th non-linear corrections in the saturation region,...
moreIn this paper, we use the re-summation procedure, suggested in Refs.\cite{DIMST,SALAM,SALAM1,SALAM2}, to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce th non-linear corrections in the saturation region, which is based on the leading twist non-linear equation. In the kinematic region:$\tau\,\equiv\,r^2 Q^2_s(Y)\,\leq\,1$ , where $r$ denotes the size of the dipole, $Y$ its rapidity and $Q_s$ the saturation scale, we found that the re-summation contributes mostly to the leading twist of the BFKL equation. Assuming that the scattering amplitude is small, we suggest using the linear evolution equation in this region. For $\tau \,>\,1$ we are dealing with the re-summation of $\Lb \bas \,\ln \tau\Rb^n$ and other corrections in NLO approximation for the leading twist.We find the BFKL kernel in this kinematic region and write the non-linear equation, which we solve analytically. We believe the new equation could be a basis for a consistent phenomenology ...
