Constraints on decay plus oscillation solutions of the solar neutrino problem

We examine the constraints on non-radiative decay of neutrinos from the observations of solar neutrino experiments. The standard oscillation hypothesis among three neutrinos solves the solar and atmospheric neutrino problems. 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 $\nu_2$, $(\tau_2/m_2) > 22.7 (\srm/\MeV)$ for the MSW solution of the solar neutrino problem and $(\tau_2/m_2) > 27.8 (\srm/\MeV)$ for the VO solution (at 99% C.L.).