are fixed by the QCD Lagrangian. Two such hadrons interact with each other by exchanging, with probability of the order of $\alpha^2$ ($\alpha$ is the strong coupling constant), one or several gluons between the partons of similar sizes and impact parameters that are present in the wavefunctions of the two hadrons at the time of the interaction.

0.1

The outline goes as follows. In the next section (Sec. \[sec2\]), we introduce a model for partonic state evolution under splittings only. Sec. \[sec3\] is devoted to the formulation of the unitary scattering amplitudes built from these states, that we compare to cases in which saturation is included explicitly in the evolution. The numerical study of the many variants of the toy model, in different frames and within different unitarization schemes, is the object of Sec. \[sec4\]. In Sec. \[sec5\] we present an alternative calculation, based on the numerical resummation of the asymptotic series in the number of Pomerons that are exchanged. We state our conclusions and some prospects in the last section.

\[sec2\]Toy model for linear parton evolution
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\[sec2A\]Construction of the model
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Focussing on one particular impact parameter, one may reduce the QCD problem to one transverse dimension only. 