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

TL;DR

This paper develops a new non-linear equation in the re-summed NLO perturbative QCD framework, focusing on the leading twist approximation and saturation effects, with potential applications in CGC phenomenology.

Contribution

It introduces a novel non-linear equation based on re-summed NLO BFKL kernel and leading twist approximation, providing an analytical solution for saturation region dynamics.

Findings

Re-summation mainly affects the leading twist of BFKL in the saturation region.

Linear evolution is valid for small scattering amplitudes when τ ≤ 1.

Derived an analytical solution for the non-linear equation in the saturation region.

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:$\tau\,\equiv\,r^2 Q^2_s(Y)\,\leq\,1$ , 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 based on the CGC approach.