Treatment of flux shape uncertainties in unfolded, flux-averaged neutrino cross-section measurements

The exact way of treating flux shape uncertainties in unfolded, flux-averaged neutrino cross-section measurements can lead to subtle issues when comparing the results to model predictions. There is a difference between reporting a cross section in the (unknown) real flux, and reporting a cross section that was extrapolated from the (unknown) real flux to a fixed reference flux. A lot of (most?) current analyses do the former, while the results are compared to model predictions as if they were the latter. This leads to (part of) the flux shape uncertainty being ignored, potentially leading to wrong physics conclusions. The size of the effect is estimated to be sub-dominant, but non-negligible in two example measurements from T2K and MINERvA. This paper describes how the issue arises and provides instructions for possible ways how to treat the flux shape uncertainties correctly.