Geometric scaling and QCD evolution

We study the impact of the QCD DGLAP evolution on the geometric scaling of the gluon distributions which is expected to hold at small x within the saturation models. To this aim we solve the DGLAP evolution equations with the initial conditions provided along the critical line Q^2=Q_s^2(x) where Q_s^2(x) = Q_0^2 x^{-λ}and satisfying geometric scaling. Both fixed and running coupling cases are studied. We show that in the fixed coupling case the geometric scaling at low x is stable against the DGLAP evolution for sufficiently large values of the parameter λand in the double logarithmic approximation of the DGLAP evolution this happens for λ> 4N_cα_s/π. In the running coupling case geometric scaling is found to be approximately preserved at very small x. The residual geometric scaling violation in this case can be approximately factored out and the corresponding form-factor controlling this violation is found.

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