Recent progress in modeling neutrino-nucleus interactions for oscillation experiments

The analysis of accelerator-based neutrino experiments crucially depends on the good control of nuclear effects in the neutrino interactions with the detectors. Recently the focus of both experimental measurements and theoretical studies has moved from the inclusive channel, where only the final lepton is detected, to the more challenging semi-inclusive reactions, where one or more hadrons are detected in coincidence with the lepton. In this contribution we present our recent research of the semi-inclusive $(ν_μ,μp)$ reaction on carbon for the quasielastic and the two-particle-two-hole channels. We show some representative results and their comparison with experimental data, illustrating the robustness of the theoretical approach and discussing possible improvements to the model.