Probing gluon saturation through inclusive hadron production in DIS

We investigate gluon saturation effects in semi-inclusive deep inelastic scattering (SIDIS) at small-$x$ within the Color Glass Condensate framework. We compute the SIDIS cross section at leading order in the dipole picture, expressing it in terms of the dipole-target scattering amplitude. We validate our framework by comparing with the charged hadron spectra measured at HERA. Our predictions for the EIC indicate that saturation effects result in significant nuclear suppression in the SIDIS cross section, and can provide complementary constraints on the initial condition for the Balitsky-Kovchegov evolution extracted from inclusive DIS data. These results demonstrate that SIDIS measurements at the EIC are sensitive to nonlinear QCD dynamics in the saturation regime.