Neutrino Mixing Constraints and Supernova Nucleosynthesis

Abstract

We reexamine the constraints on mixing between electron and muon or tau neutrinos from shock-reheating and r-process nucleosynthesis in supernovae. To this end neutrino flavor evolution is described by nonlinear equations following from a quantum kinetic approach. This takes into account neutrino forward scattering off the neutrino background itself. In contrast to other claims in the literature it is shown that a sound self-consistent analytical approximation can in the first place only be performed in the adiabatic limit where phase terms are suppressed. In the cosmologically interesting mass range below about $25\eV$ the resulting mixing parameter bounds are between one and two orders of magnitude less restrictive than limits neglecting neutrino contributions. Extensions to the non-adiabatic regime derived in the literature usually neglect coherence effects from phases. To check their importance numerical simulations of the evolution equations were performed in this regime. They indicate that analytical approximations for the flavor conversion efficiencies can indeed be extended by neglecting phase terms. This allows more stringent bounds similar to the ones derived in earlier work. These bounds depend to some extent on the adopted supernova model and tend to be somewhat less restrictive in the mixing angle but simultaneously extend to smaller mixing masses compared to limits neglecting the neutrino induced potential.