Confronting next-to-leading order CGC/Saturation approach with HERA data

In this talk, we present an analysis of the next-to-leading order CGC/saturation approach from Ref.~\cite{CLMS} using combined HERA data to determine its parameters. The model features an analytical solution for the non-linear Balitsky-Kovchegov (BK) evolution equation and an exponential behavior of the saturation momentum with impact parameter $b$-dependence, characterized by $Q_s \propto \exp(-mb)$. With its parameters fixed via a fit to high-precision HERA data, we compare the model predictions with experimental data at small-$x$ for the proton structure function $F_2$, longitudinal structure function $F_L$ and exclusive vector meson production. The model shows excellent agreement across a wide kinematic range of $Q^2$ at small-$x$, supporting its use for reliable predictions in upcoming experiments like the Electron-Ion Collider and the LHeC.