  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.
