in opposite directions in order to increase the center-of-mass energy of their eventual scattering, the probability of a high number of partons in each of them increases. At some point, when the unitarity limit is reached (as soon as the total rapidity is larger than $y_F$), the probability that there be two or more interactions between them becomes of order 1, while each of the Fock states remains relatively dilute (they contain only typically $1/\alpha$ particles each), in such a way that one can still consider their evolution as linear. Actually, because the systems share half of the rapidity, they become subject to nonlinear effects (in the form of internal rescatterings, for instance, or recombinations) at rapidity $2\times y_F$. So this sets the limit beyond which multiple interactions between linearly-evolving Fock states are no longer sufficient to fully describe the scattering. The extension to an arbitrary value of $\sigma$ is straightforward, and we get the limit $$y<\frac{y_F}{\max(\sigma,1-\sigma)}.$$ The center-of-mass frame ($\sigma=\frac12$) is naturally the most favorable case, with the highest limit on $y$, while in the lab frame, the wavefunction evolution can be linear only until blackness of the scattering amplitude is reached.

\[sec3B\]Saturation
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So far, we have considered 