Exploring the DGLAP resummation in the JIMWLK Hamiltonian

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 $\ln Q^2\mathrm{/}{Q}_s^2$. Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.