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

Abstract

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