Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation

Abstract

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, which is based on the leading twist non-linear equation. In the kinematic region:$\tau \equiv r^2{Q}_s^2(Y)\le 1$ , 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 $\text{Lb}\text{bas}\ln \tau {\text{Rb}}^n$ 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 based on the CGC approach.

Comments: 22pp. 12 figures in pdf files