We investigate the potential for the Deep Underground Neutrino Experiment (DUNE) to probe the existence and effects of a fourth neutrino mass-eigenstate. We study the mixing of the fourth mass-eigenstate with the three active neutrinos of the Standar
d Model, including the effects of new sources of CP-invariance violation, for a wide range of new mass-squared differences, from lower than 10^-5 eV^2 to higher than 1 eV^2. DUNE is sensitive to previously unexplored regions of the mixing angle - mass-squared difference parameter space. If there is a fourth neutrino, in some regions of the parameter space, DUNE is able to measure the new oscillation parameters (some very precisely) and clearly identify two independent sources of CP-invariance violation. Finally, we use the hypothesis that there are four neutrino mass-eigenstates in order to ascertain how well DUNE can test the limits of the three-massive-neutrinos paradigm. In this way, we briefly explore whether light sterile neutrinos can serve as proxies for other, in principle unknown, phenomena that might manifest themselves in long-baseline neutrino oscillation experiments.
We explore, mostly using data from solar neutrino experiments, the hypothesis that the neutrino mass eigenstates are unstable. We find that, by combining $^8$B solar neutrino data with those on $^7$Be and lower-energy solar neutrinos, one obtains a m
ostly model-independent bound on both the $ u_1$ and $ u_2$ lifetimes. We comment on whether a nonzero neutrino decay width can improve the compatibility of the solar neutrino data with the massive neutrino hypothesis.
Neutrino propagation in space-time is not constrained to be unitary if very light states - lighter than the active neutrinos - exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing
and oscillation parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature.
