Longitudinal kinematic imbalances in neutrino and antineutrino interactions for improved measurements of neutrino energy and the axial vector form factor

Current and future accelerator neutrino oscillation experiments require an improved understanding of nuclear effects in neutrino-nucleus interactions. One important systematic uncertainty is introduced by the collective impact of nuclear effects which bias the reconstruction of the neutrino energy, such as the nuclear removal energy. In this manuscript, we introduce a novel observable for accelerator neutrino oscillation experiments, the visible longitudinal momentum imbalance, reconstructed in charged current quasi-elastic interactions from the outgoing charged lepton and nucleon. We demonstrate it to be minimally dependent on the neutrino energy and sensitive to sources of bias in neutrino energy reconstruction. Furthermore, we show how the use of the longitudinal imbalance in antineutrino interactions in a target containing hydrogen allows for an improved, high-purity selection of the interactions on hydrogen. This approach offers the potential for precise measurements of the nuclear axial vector form factor as well as of the antineutrino flux.