Exploring the DGLAP resummation in the JIMWLK Hamiltonian

TL;DR

This paper investigates the impact of DGLAP resummation on the JIMWLK Hamiltonian within SU(2) gauge theory, revealing universal patterns in unitarity deviations during gluon scattering simulations.

Contribution

It introduces a numerical analysis of the DGLAP-resummed JIMWLK equation in SU(2), highlighting universal unitarity deviations in gluon scattering.

Findings

Unitarity of the gluon S-matrix breaks down at high ln Q^2/Q_s^2.

Universal pattern observed in unitarity deviation, independent of coupling.

Numerical solutions demonstrate the behavior of dressed gluon scattering.

Abstract

We explore the recently derived equation that resums DGLAP corrections to the JIMWLK Hamiltonian in the simplified setting of the SU(2) gauge theory. We solve the equation numerically for the scattering matrix of a dressed gluon for a particular initial condition, that corresponds to a dipole initial state. As expected, the $S$-matrix of a single dressed gluon state ceases to be unitary if evolved to significant $\ln Q^2/Q_s^2$. Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.