  As accelerator-neutrino oscillation experiments improve oscillation parameter
constraints, 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 processes to avoid introducing bias. One option discussed
in this context is the "low-$\nu$" method, designed to isolate neutrino
interactions where there is low energy-transfer to the nucleus, such that the
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 few-GeV energies of current and future accelerator neutrino
experiments remains unclear due to the presence of nuclear and form-factor
effects.
  In this analysis we examine the prospects for improving constraints on
accelerator neutrino fluxes 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. The
results show that flux constraints from the low-$\nu$ method would be severely
dependent on the specific interaction model assumptions used in an analysis for
neutrino energies less than 5 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.
