A substandard candle: the low-$\nu $ method at few-GeV neutrino energies

As accelerator-based neutrino oscillation experiments improve oscillation parameter constraints with more data, control over systematic uncertainties on the incoming neutrino flux and interaction models is increasingly important. The intense beams offered by modern experiments permit a variety of options to constrain the flux using in situ “standard candle” measurements. These standard candles must use very well understood interaction processes to avoid introducing additional interaction model dependence. One option often discussed in this context is the “low-$\nu $ ” method, which is designed to isolate neutrino interactions where there is low energy-transfer to the nucleus, such that the interaction cross section is expected to be approximately constant as a function of neutrino energy. The shape of the low-energy transfer event sample can then be used to extract the flux shape. Applications of the method at high neutrino energies (many tens of GeV) are well understood. However, the applicability of the method at the lower energies of current and future few-GeV accelerator neutrino experiments remains unclear due to the presence of nuclear and form-factor effects inherent in the interaction models.In this analysis we examine the prospects for improving constraints on the accelerator neutrino fluxes in situ with the low-$\nu $ method in an experiment-independent way, using (anti)neutrino interactions on argon and hydrocarbon targets from the GENIE, NEUT, NuWro and GiBUU event generators. We begin by investigating the extent to which deviations from the constant cross-section assumption are dependent on poorly understood aspects of the neutrino interaction model. We then assess whether a low energy-transfer event sample can be confidently identified using experimentally accessible observables. We finally consider how the practicalities of reconstructing the energy spectrum of interacting neutrinos in realistic detectors might further limit the utility of low-$\nu $ flux constraints. The results show that flux constraints from the low-$\nu $ method would be severely dependent on the interaction model assumptions used in an analysis of neutrinos with energies below 5 GeV, and anti-neutrinos below at least 15 GeV. The spread of model predictions show that a low-$\nu $ analysis is unlikely to offer much improvement on typical neutrino flux uncertainties, even with a perfect detector. Notably—running counter to the assumption inherent to the low-$\nu $ method—the model-dependence increases with decreasing energy transfer for experiments in the few-GeV region.