Probing the saturation effects in the inclusives observables at the future ep/eA collider at the LHC

In this paper we investigate the impact of the saturation effects in the inclusive observables that will be measured in the future Large Hadron Electron Collider (LHeC). The reduced total and heavy quark cross sections are estimated considering the more recent phenomenological models for the dipole-proton scattering amplitude, which are based on the Color Glass Condensate formalism and are able to describe the inclusive and exclusive ep HERA data. We compare, for the first time, the predictions of these models with the recent combined H1 and ZEUS data for the charm and bottom production, and present predictions for the reduced cross sections considering the kinematical range that will be probed in ep collisions at the LHeC. Moreover, we estimate the magnitude of the saturation effects for the nuclear, longitudinal and charm structure functions in the case of eA collisions at the LHeC. Our results indicate that the future experimental data will be useful to discriminate between the different models for the nonlinear QCD dynamics.