Final state interactions in semi-inclusive neutrino-nucleus scattering: Application to T2K and MINER$\nu$A experiments

We present a complete comparison of semi-inclusive <math display="inline"><mrow><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mtext>-</mtext><mmultiscripts><mrow><mi mathvariant="normal">C</mi></mrow><mprescripts/><none/><mrow><mn>12</mn></mrow></mmultiscripts></mrow></math> cross section measurements by T2K and <math display="inline"><mi>MINER</mi><mi>ν</mi><mi mathvariant="normal">A</mi></math> collaborations with the predictions from the SuSAv2-MEC model implemented in the neutrino-nucleus event generator GENIE and an unfactorized approach based on the relativistic distorted wave impulse approximation. Results, that include cross sections as function of the final muon and proton kinematics and correlations between both, show that the agreement with data obtained by the relativistic distorted wave impulse approximation approach, that accounts for final-state interactions, matches or improves GENIE-SuSAv2 predictions for very forward angles where scaling violations are relevant.