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This paper reports measurements of final-state proton multiplicity, muon and proton kinematics, and their correlations in charged-current pionless neutrino interactions, measured by the T2K ND280 near detector in its plastic scintillator (C 8 H 8 ) target. The data were taken between years 2010 and 2013, corresponding to approximately 6 × 10 20 protons on target. Thanks to their exploration of the proton kinematics and of imbalances between the proton and muon kinematics, the results offer a novel probe of the nuclear-medium effects most pertinent to the (sub-)GeV neutrino-nucleus interactions that are used in accelerator-based long-baseline neutrino oscillation measurements. These results are compared to many neutrino-nucleus interaction models which all fail to describe at least part of the observed phase space. In case of events without a proton above a detection threshold in the final state, a fully consistent implementation of the local Fermi gas model with multinucleon interactions gives the best description of the data. In the case of at least one proton in the final state, the spectral function model agrees well with the data, most notably when measuring the kinematic imbalance between the muon and the proton in the plane transverse to the incoming neutrino. Within the models considered, only the existence of multinucleon interactions are able to describe the extracted cross section within regions of high transverse kinematic imbalance. The effect of final-state interactions is also discussed.

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Background: Neutrino-induced single-pion production (SPP) provides an important contribution to neutrino-nucleus interactions, ranging from intermediate to high energies. There exists a good number of low-energy models in the literature to describe the neutrinoproduction of pions in the region around the Delta resonance. Those models consider only lowest-order interaction terms and, therefore, fail in the high-energy region (pion-nucleon invariant masses, W 2 GeV).Purpose: Our goal is to develop a model for electroweak SPP off the nucleon, which is applicable to the entire energy range of interest for present and future accelerator-based neutrino-oscillation experiments.Method: We start with the low-energy model of Ref.[1], which includes resonant contributions and background terms derived from the pion-nucleon Lagrangian of chiral-perturbation theory [2]. Then, from the background contributions, we build a high-energy model using a Regge approach. The low-and highenergy models are combined, in a phenomenological way, into a hybrid model. Results:The Hybrid model is identical to the low-energy model in the low-W region, but, for W > 2 GeV, it implements the desired high-energy behavior dictated by Regge theory. We have tested the high-energy model by comparing with one-pion production data from electron and neutrino reactions. The Hybrid model is compared with electron-proton scattering data, with neutrino SPP data and with the predictions of the NuWro Monte Carlo event generator. Conclusions: Our model is able to provide satisfactory predictions of the electroweak one-pion production cross section from pion threshold to high W . Further investigation and more data are needed to better understand the mechanisms playing a role in the electroweak SPP process in the high-W region, in particular, those involving the axial current contributions.