Unfolding the low-energy reactor neutrino flux from CE$ν$NS data with a finite Dirac sum

Abstract: We present a novel method to analyze coherent elastic neutrino--nucleus scattering (CE$ν$NS) data to extract the reactor antineutrino spectrum below the inverse beta decay threshold of 1.8 MeV, where it remains unmeasured. Adapting halo-independent analysis techniques developed for direct dark matter detection, we show how to obtain a best-fit and a pointwise confidence band for the integrated neutrino flux, without assuming a parametric form or smoothness prior for the spectrum. In our approach, which follows from convex geometry arguments, the differential neutrino rate is written as a linear combination of Dirac delta functions -- a finite Dirac sum (FDS) -- with a maximum number of terms determined by the number of data points. We apply our ``FDS method'' to mock CE$ν$NS data for a low-threshold Ge detector and compare it with Tikhonov-regularized unfolding.