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Double- and single-differential cross sections for inclusive charged-current ${\nu }_{\mu }$-nucleus scattering are reported for the kinematic domain 0 to $2\mathrm{GeV}/c$in three-momentum transfer and 0 to 2 GeV in available energy, at a mean ${\nu }_{\mu }$energy of 1.86 GeV. The measurements are based on an estimated 995,760 ${\nu }_{\mu }$charged-current (CC) interactions in the scintillator medium of the NOvA Near Detector. The subdomain populated by 2-particle-2-hole (2p2h) reactions is identified by the cross section excess relative to predictions for ${\nu }_{\mu }$-nucleus scattering that are constrained by a data control sample. Models for 2-particle-2-hole processes are rated by ${\chi }^2$comparisons of the predicted-versus-measured ${\nu }_{\mu }$CC inclusive cross section over the full phase space and in the restricted subdomain. Shortfalls are observed in neutrino generator predictions obtained using the theory-based València and SuSAv2 2p2h models. Published by the American Physical Society2025 

Abstract Measuring observables to constrain models using maximum-likelihood estimation is fundamental to many physics experiments. Wilks' theorem provides a simple way to construct confidence intervals on model parameters, but it only applies under certain conditions. These conditions, such as nested hypotheses and unbounded parameters, are often violated in neutrino oscillation measurements and other experimental scenarios. Monte Carlo methods can address these issues, albeit at increased computational cost. In the presence of nuisance parameters, however, the best way to implement a Monte Carlo method is ambiguous. This paper documents the method selected by the NOvA experiment, the profile construction. It presents the toy studies that informed the choice of method, details of its implementation, and tests performed to validate it. It also includes some practical considerations which may be of use to others choosing to use the profile construction.