https://doi.org/10.1140/epjc/s10052-020-08580-w
Regular Article – Theoretical Physics
Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation
1
Departamento de Física, Universidad Técnica Federico Santa María, Avda. España 1680, Casilla 110-V, Valparaiso, Chile
2
Centro Científico-Tecnológico de Valparaíso, Avda. España 1680, Casilla 110-V, Valparaiso, Chile
3
Department of Particle Physics, School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University, 69978, Tel Aviv, Israel
4
Escuela de Ingeniería Civil, Facultad de Ingeniería, Universidad de Valparaíso, General Cruz 222, Valparaiso, Chile
b leving@tauex.tau.ac.il, eugeny.levin@usm.cl
Received:
23
July
2020
Accepted:
19
October
2020
Published online:
6
November
2020
In this paper, we use the re-summation procedure, suggested in Ducloué et al. (JHEP 1904:081, 2019), Salam (JHEP 9807:019 1998), Ciafaloni et al. (Phys Rev D 60:1140361999) and Ciafaloni et al. (Phys Rev D 68:114003, 2003), to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce the non-linear corrections in the saturation region, which is based on the leading twist non-linear equation. In the kinematic region: 
, where r denotes the size of the dipole, Y its rapidity and 
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 
we are dealing with the re-summation of 
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.
© The Author(s) 2020
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