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In this paper we show that the intuitive guess that the geometric scalingbehaviour should be violated in the case of the running QCD coupling, turns outto be correct. The scattering amplitude of the dipole with the size $r$ dependson new dimensional scale: $\Lambda_{QCD}$, even at large values $Y = \ln(1/x)$and $l\,=\, \ln\Lb \as\Lb r^2\Rb/\as\Lb 1/Q^2_s\Rb\Rb$. However, in this regionwe found a new scaling behaviour: the amplitude is a function of $\zeta =Y\,l$. We state that only in the vicinity of the saturation scale $Q_s$($\as(Q^2_s)\,\ln \Lb r^2 Q^2_s\Rb\,\leq \, 1$), the amplitude shows thegeometric scaling behaviour. Based on these finding the geometric scalingbehavior that has been seen experimentally, stems from either we have notprobed the proton at HERA and the LHC deeply inside the saturation region orthat there exists the mechanism of freezing of the QCD coupling constant at$r^2 \approx 1/Q^2_s$.

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