Abstract
The increasing of the gluon distribution at small - $x$ implies that the hadrons are characterized by a high partonic density and that non - linear (saturation) effects in the QCD dynamics cannot be disregarded at high energies. The evolution with the rapidity of the high density system is described by the Balitsky - Kovchegov (BK) equation. In this contribution, we consider the recent results for the next - to - leading order corrections to the BK equation and derive its asymptotic solution in the saturation regime assuming that the hard scale is the saturation scale. A detailed comparison with the solutions obtained assuming other prescriptions for the hard scale is presented.
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