Decaying neutrinos and implications from the supernova relic neutrino observation

We propose that supernova relic neutrino (SRN) observation can be used to set constraints on the neutrino decay models. Because of the long distance scale from cosmological supernovae to the Earth, SRN have possibility to provide much stronger limit than the present one obtained from solar neutrino observation. Since the currently available data are only the upper limit on the flux integrated over $E_{\bar\nu_e}>19.3$ MeV, the decay models on which we can set constraints is quite restricted; they must satisfy specific conditions such that the daughter neutrinos are active species, the neutrino mass spectrum is quasi-degenerate, and the neutrino mass hierarchy is normal. Our numerical calculation clearly indicates that the neutrino decay model with $(\tau_2/m,\tau_3/m)\alt (10^{10},10^{10})$ [s/eV], where $\tau_i$ represents the lifetime of mass eigenstates $\bar\nu_i$, appears to give the SRN flux that is larger than the current upper limit. However, since the theoretical SRN prediction contains many uncertainties concerning a supernova rate in the universe or simulation of supernova explosions, we cannot conclude that there exists the excluded parameter region of the neutrino lifetime. In the near future, further reduced upper limit is actually expected, and it will provide more severe constraints on the neutrino decay models.