Violation of the geometric scaling behavior of the amplitude for running QCD coupling in the saturation region

In this paper we show that the intuitive guess that the geometric scaling behavior should be violated in the case of the running QCD coupling, turns out to be correct. The scattering amplitude of the dipole with the size r depends on new dimensional scale: Λ_QCD, even at large values Y=ln(1/x) and l=ln(αS(r²)/αS(1/Q_s²)). However, in this region we found a new scaling behavior: the amplitude is a function of ζ=Yl. We state that only in the vicinity of the saturation scale Q_s (α_s(Q_s²)ln(r²Q_s²)≤1), the amplitude shows the geometric scaling behavior. Based on these finding the geometric scaling behavior that has been seen experimentally, stems from either we have not probed the proton at HERA and the LHC deeply inside the saturation region or that there exists the mechanism of freezing of the QCD coupling constant at r²≈1/Q_s².