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Simultaneous measurement of proton and lepton kinematics in quasielastic-like $ν_μ$-hydrocarbon interactions from 2 to 20 GeV

Neutrino charged-current quasielastic-like scattering, a reaction category extensively used in neutrino oscillation measurements, probes nuclear effects that govern neutrino-nucleus interactions. This Letter reports the first measurement of the triple-differential cross section for $ν_μ$ quasielastic-like reactions using the hydrocarbon medium of the MINERvA detector exposed to a wide-band beam spanning 2 $\leq$ E$_ν\leq$ 20 GeV. The measurement maps the correlations among transverse and longitudinal muon momenta and summed proton kinetic energies, and compares them to predictions from a state-of-art simulation. Discrepancies are observed that likely reflect shortfalls with modeling of pion and nucleon intranuclear scattering and/or spectator nucleon ejection from struck nuclei. The separate determination of leptonic and hadronic variables can inform experimental approaches to neutrino-energy estimation.