QCD traveling waves phenomenology revisited

In this paper we review and update the Amaral-Gay Ducati-Betemps-Soyez saturation model, by testing it against the recent H1-ZEUS combined data on deep inelastic scattering, including heavy quarks in the dipole amplitude. This model, based on traveling wave solutions of the Balitsky-Kovchegov equation and built in the momentum space framework, yields very accurate descriptions of the reduced cross section, $\sigma_{r}(x,y,Q^{2})$, measured at HERA as well as DIS structure functions such as $F_{2}(x,Q^{2})$ and $F_{L}(x,Q^{2})$. Additionally, it provides reasonable descriptions of heavy quark structure functions, $F_{2}^{cc}$ and $F_{2}^{bb}$ at small-$x$ and $Q^{2}\lesssim 60$ GeV$^{2}$. Having obtained excellent agreement with HERA data we use the improved model to make predictions for structure functions to be measured in the near future at LHeC.