Not all that is $\beta_0$ is $\beta$-function: the DGLAP resummation and the running coupling in NLO JIMWLK

TL;DR

This paper clarifies the origin of large transverse logarithms in NLO JIMWLK evolution, distinguishing those from the beta-function and DGLAP evolution, and derives a nonlinear RG equation to resum these effects across different regimes.

Contribution

It introduces a DGLAP-like resummation within the NLO JIMWLK Hamiltonian, clarifying the source of large logarithms and deriving an all-orders nonlinear RG equation for the scattering matrix.

Findings

Resummation of large transverse logarithms is necessary for accurate JIMWLK evolution.

Derived a nonlinear RG equation that resums these logarithms to all orders in alpha_s.

Solved the RG equation in dilute and saturated regimes, demonstrating the impact of DGLAP resummation.

Abstract

We reanalyze the origin of the large transverse logarithms associated with the QCD one loop beta-function coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders in alpha_s in the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrix S(x). We solve this equation and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum.