Confronting impact-parameter dependent model in next-to-leading order of perturbative QCD with combined HERA data

In this talk, we present the CGC/saturation approach of Ref.[C.~Contreras, E.~Levin, R.~Meneses and M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029] and its parameters determined from the combined HERA data. This model features an analytical solution for the non-linear Balitsky-Kovchegov (BK) evolution equation and the exponential behavior of the saturation momentum on the impact parameter $b$-dependence, characterized by $Q_s\propto \exp(-mb)$. We compare our results with experimental data at small-$x$, including the proton structure function $F_2$, charm structure function $F_2^{c\bar{c}}$, and exclusive vector meson production. The model shows good agreement across a wide kinematic range. Our findings support using this approach for reliable predictions in upcoming experiments like the Electron-Ion Collider (EIC) and the LHeC.