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In this paper we confront the CGC/saturation approach of Ref.~\cite{CLMS}with the experimental combined HERA data and obtain its parameters. The modelincludes two features that are in accordance with our theoretical knowledge ofdeep inelastic scattering. These consist of: \textit{i}) the use of analyticalsolution for the non-linear Balitsky-Kovchegov (BK) evolution equation and\textit{ii}) the exponential behavior of the saturation momentum on the impactparameter $b$-dependence, characterized by $Q_s$ $\propto\exp(-mb)$ whichreproduces the correct behavior of the scattering amplitude at large $b$ inaccord with Froissart theorem. The model results are then compared to data atsmall-$x$ for the structure-function of the proton $F_{2}$, the longitudinalstructure function $F_{L}$, the charm structure function $F_2^{c\bar{c}}$, theexclusive vector meson ($J/\psi,\phi,\rho$) production and Deeply VirtualCompton Scattering (DVCS). We obtain a good agreement for the processes in awide kinematic range of $Q^2$ at small-$x$. Our results provide a strong guidefor finding an approach, based on Color Glass Condensate/saturation effectivetheory for high energy QCD, to make reliable predictions from first principlesand for forthcoming experiments like the Electron-Ion Collider and the LHeC.

CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data