Constraints on decay plus oscillation solutions of the solar neutrino problem

We examine the constraints on the nonradiative decay of neutrinos from the observations of solar neutrino experiments. The standard oscillation hypothesis among three neutrinos solves the solar and atmospheric neutrino problems. The decay of a massive neutrino mixed with the electron neutrino results in the depletion of the solar neutrino flux. We introduce neutrino decay in the oscillation hypothesis and demand that decay does not spoil the successful explanation of solar and atmospheric observations. We obtain a lower bound on the ratio of the lifetime over the mass of ν₂, τ₂/m₂>22.7s/MeV for the Mikheyev-Smirnov-Wolfenstein solution of the solar neutrino problem and τ₂/m₂>27.8s/MeV for the vacuum oscillation solution (at $99%$ C.L.).