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. We obtain that this model, which is 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, ${\ensuremath{\sigma}}_{r}(x,y,{Q}^{2})$, as well as DIS structure functions such as ${F}_{2}(x,{Q}^{2})$ and ${F}_{L}(x,{Q}^{2})$, all measured at HERA. Additionally, it provides good descriptions of heavy quark structure functions, ${F}_{2}^{cc}$ and ${F}_{2}^{bb}$ at small-$x$ and ${Q}^{2}\ensuremath{\lesssim}60\text{ }\text{ }{\mathrm{GeV}}^{2}$. We also use the improved model to make predictions for structure functions to be measured in the near future at LHeC.