Reactor Neutrino Spectral Distortions Play Little Role in Mass Hierarchy Experiments

The Coulomb enhancement of low energy electrons in nuclear beta decay generates sharp cutoffs in the accompanying antineutrino spectrum at the beta decay endpoint energies. It has been conjectured that these features will interfere with measuring the effect of a neutrino mass hierarchy on an oscillated nuclear reactor antineutrino spectrum. These sawtooth-like features will appear in detailed reactor antineutrino spectra, with characteristic energy scales similar to the oscillation period critical to neutrino mass hierarchy determination near a 53 km baseline. However, these sawtooth-like distortions are found to contribute at a magnitude of only a few percent relative to the mass hierarchy-dependent oscillation pattern in Fourier space. In the Fourier cosine and sine transforms, the features that encode a neutrino mass hierarchy dominate by over sixteen (thirty-three) times in prominence to the maximal contribution of the sawtooth-like distortions from the detailed energy spectrum, given $3.2%/sqrt{E_mathrm{vis.}/mathrm{MeV}}$ (perfect) detector energy resolution. The effect of these distortions is shown to be negligible even when the uncertainties in the reactor spectrum, oscillation parameters, and counting statistics are considered. This result is shown to hold even when the opposite hierarchy oscillation patterns are nearly degenerate in energy space, if energy response nonlinearities are controlled to below 0.5%. Therefore with accurate knowledge of detector energy response, the sawtooth-like features in reactor antineutrino spectra will not significantly impede neutrino mass hierarchy measurements using reactor antineutrinos.