https://doi.org/10.1140/epjc/s10052-019-7363-6
Regular Article - Theoretical Physics
BFKL equation in the next-to-leading order: solution at large impact parameters
1
Departamento de Física, Universidad Técnica Federico Santa María, and Centro Científico-Tecnológico de Valparaíso, Avda. España 1680, Casilla 110-V, Valparaíso, Chile
2
Department of Particle Physics, School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Science, Tel Aviv University, 69978, Tel Aviv, Israel
3
Escuela de Ingeniería Civil, Facultad de Ingeniería, Universidad de Valparaíso, General Cruz 222, Valparaíso, Chile
* e-mail: leving@tauex.tau.ac.il
** e-mail: eugeny.levin@usm.cl
Received:
3
July
2019
Accepted:
1
October
2019
Published online:
11
October
2019
In this paper, we show (1) that the NLO corrections do not change the power-like decrease of the scattering amplitude at large impact parameter (
, where r denotes the size of scattering dipole and 
for DIS), and, therefore, they do not resolve the inconsistency with unitarity; and (2) they lead to an oscillating behaviour of the scattering amplitude at large b, in direct contradiction with the unitarity constraints. However, from the more practical point of view, the NLO estimates give a faster decrease of the scattering amplitude as a function of b, and could be very useful for description of the experimental data. It turns out, that in a limited range of b, the NLO corrections generates the fast decrease of the scattering amplitude with b, which can be parameterized as 
with 
in accord with the numerical estimates in Cepila et al. (Phys Rev D 99(5):051502, https://doi.org/10.1103/PhysRevD.99.051502, arXiv:1812.02548 [hep-ph], 2019).
© The Author(s), 2019
