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

TL;DR

This paper introduces a modified evolution equation for QCD scattering amplitudes that allows continuous adjustment of the pre-asymptotic RG flow towards unitarity, facilitating phenomenological comparisons and potential observational constraints.

Contribution

It proposes a new evolution equation that preserves key fixed points and is suitable for numerical analysis, enabling comparisons with existing QCD flow models.

Findings

The evolution equation maintains the unitarity limit attractor.

It is suitable for efficient numerical solutions.

Single-inclusive spectra at RHIC do not strongly constrain the flow.

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.