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Scattering amplitudes in QCD exhibit a definite RG flow with energy towardsthe unitarity limit. In this paper we put forward an evolution equation whichallows one to modify continuously the pre-asymptotic RG flow towards"saturation" of Wilson line correlators. It preserves the linearly unstablezero field fixed point and the unitarity limit attractor. We present theevolution equations in a form suitable for efficient numerical solution. Hence,the proposed evolution equation in principle permits phenomenologicalcomparisons of our incorrect pre-asymptotic RG flows to the BK/JIMWLK flow ofQCD. Ultimately, it may lead to observational constraints on the approach tounitarity, constraining it to be specifically the one of QCD. However, itappears that single-inclusive particle spectra in the forward region of p+Acollisions at RHIC alone do not provide stringent constraints on the evolution.

An incorrect pre-asymptotic RG flow of scattering amplitudes in QCD towards the unitarity limit