Neutrino mass spectrum from the results of neutrino oscillation experiments
S. M. Bilenky, C. Giunti, W. Grimus
TL;DR
This work evaluates which four-neutrino mass spectra can coherently accommodate solar, atmospheric, and LSND oscillation hints, using a model-independent approach and the assumption that short-baseline oscillations are governed by a single $\Delta m^2$. It shows that a hierarchical four-neutrino spectrum is incompatible with the global data, and that spectra with two nearly degenerate pairs separated by $\sim 1\,\mathrm{eV}$ (spectra (A) and (B)) remain viable. These two schemes differ in their predictions for $^3$H beta-decay endpoint masses and for neutrinoless double-beta decay, offering a path to experimental discrimination and implying the necessity of at least one sterile neutrino. The results highlight a mass spectrum distinct from that of charged fermions, underscoring the need for beyond-three-neutrino explanations to reconcile all oscillation observations.
Abstract
All the possible schemes of neutrino mixing with four massive neutrinos inspired by the existing experimental indications in favor of neutrino mixing are considered in a model independent way. Assuming that in short-baseline experiments only one mass-squared difference is relevant, it is shown that the scheme with a neutrino mass hierarchy is not compatible with the experimental results. Only two schemes with two pairs of neutrinos with close masses separated by a mass difference of the order of 1 eV are in agreement with the results of all experiments. One of these schemes leads to possibly observable effects in Tritium and neutrinoless double-beta decay experiments.