  We present the results of semi-inclusive neutrino-nucleus cross sections
within the plane wave impulse approximation (PWIA) for three nuclear models:
relativistic Fermi gas (RFG), independent-particle shell model (IPSM) and
natural orbital shell model (NO) in comparison with the available CC0$\pi$
measurements from the T2K, MINER$\nu$A and MicroBooNE collaborations where a
muon and at least one proton are detected in the final state. Results are
presented as a function of the momenta and angles of the final particles, as
well as in terms of the imbalances between proton and muon kinematics. The
analysis reveals that contributions beyond PWIA are crucial to explain the
experimental measurements and that the study of correlations between
final-state proton and muon kinematics can provide valuable information on
relevant nuclear effects such as the Fermi motion and final state interactions.
