  The perturbative QCD predicts that the growth of the gluon density at
small-$x$ (high energies) should saturate, forming a Color Glass Condensate
(CGC), which is described in mean field approximation by the Balitsky-Kovchegov
(BK) equation. Recently, the next-to-leading order corrections for the BK
equation were derived and a global fit of the inclusive $ep$ HERA data was
performed, resulting in a parameterization for the forward scattering
amplitude. In this paper we compare this parameterization with the predictions
of other phenomenological models and investigate the saturation physics in
diffractive deep inelastic electron-proton scattering and in the forward hadron
production in $pp$ collisions. Our results demonstrate that the running
coupling BK solution is able to describe these observables.
