First Measurement of the Superscaling Variable as a Function of Visible Kinematics in Charged-Current Quasi-Elastic Neutrino--Nucleus Scattering
We report the first measurement of the superscaling variable $ψ^{\prime}_{\rm vis}$ in neutrino--nucleus scattering, using charged-current quasielastic-like $ν_μ$-Carbon interactions collected by the MINERvA experiment in the medium-energy NuMI beam. Originally developed to characterize phenomena of scaling with respect to atomic number and momentum transfer in quasielastic electron-nucleus scattering, $ψ^{\prime}$ is reconstructed here from visible final-state kinematics ($ψ^{\prime}_{\rm vis}$). $ψ^{\prime}_{\rm vis}$ is used here as an externally calibrated variable whose peak position is sensitive to the invisible nuclear missing energy. We measure $ψ^{\prime}_{\rm vis}$ as functions of the hadronic recoil $ΣT_p$ and muon transverse momentum $p_{\text{T}μ}$, comparing background-subtracted data to five neutrino--nucleus interaction models via a forward-folding technique. The predicted $ψ^{\prime}_{\rm vis}$ diverges most strongly among model predictions at low $ΣT_p$ and $p_{\text{T}μ}$, where agreement with data is also poorest, exposing which models fail to capture the phase-space dependence of the missing energy and therefore the neutrino energy as extrapolated from visible kinematics. Among tested models, we find that the Relativistic Mean Field approach predicts more accurately the $ψ^{\prime}_{\rm vis}$ peak position.