A calculation of the two-particle two-hole contribution to the semi-inclusive $({\nu }_{\mu },{\mu }^{-}N)$ cross section on carbon is performed in the framework of the relativistic Fermi gas model. The process is driven by meson-exchange currents encompassing all contributions involving the exchange of a single pion and the excitation of a $\mathrm{\Delta }$ resonance. The calculation is validated against the inclusive $({\nu }_{\mu },{\mu }^{-})$ response functions already existing in the literature, and then extended for the first time to the semi-inclusive channel. Results are presented both at fixed neutrino energy and folded with the T2K neutrino flux.

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• Electroweak interactions in nuclear physics
• Lepton induced nuclear reactions
• Nuclear reactions