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A numerical solution is presented for the non-linear evolution equation that governs the dynamics of high parton density QCD. It is shown that the solution falls off as e −b/R at large values of the impact parameter b. The power-like tail of the amplitude appears in impact parameter distributions only after the inclusion of dipoles of size larger than the target, a configuration for which the non-linear equation is not valid. The value, energy and impact parameter of the saturation scale Q s (y = ln(1/x), b)) are calculated both for fixed and running QCD coupling cases. It is shown that the solution exhibits geometrical scaling behaviour. The radius of interaction increases as the rapidity in accordance with the Froissart theorem. The solution we obtain differs from previous attempts, where an anzatz for b behaviour was made. The solutions for running and fixed α s differ. For running α s we obtain a larger radius of interaction ( approximately twice as large), a steeper rapidity dependence, and a larger value of the saturation scale.

We propose a modified version of the Balitsky-Kovchegov (B-K) evolution equation, which includes the main NLO corrections. We use the result that the main NLO corrections to the BFKL kernel are the LO DGLAP corrections. We present a numerical solution of the modified nonlinear equation, and compare with the solution of the unmodified B-K equation. We show that the saturation momentum has a sharp increase in the LHC energy range. Our numerical solution shows that the influence of the pre-asymptotic corrections, related to the full anomous dimensions of the DGLAP equation, are rather large. These corrections moderate the energy behaviour of the amplitude, as well as the value of the saturation scale. All our calculations are made with a fixed value of α s .

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Recent experimental results emanating from HERA support the supposition that we are encountering phenomena associated with high-density partons. Evidence for this is: (a) the large value of the gluon structure function; (b) the asymptotic predictions of high-density quantum chromodynamics seem to be realized. We propose a model based on the Glauber-Mueller eikonal formalism, which incorporates screening corrections. Numerical estimates calculated using this model are consistent with the experimental data, and in addition provide a natural explanation for the size of the deviation from the standard DGLAP result. To obtain a complete picture we review some of our previous results pertaining to the logarithmic slope of F 2 , and the inclusive production of J / . Alternative approaches which deal with saturation phenomena are discussed, and new experiments are suggested.