Improved cosmological and radiative decay constraints on neutrino masses and lifetimes

The best upper bounds on the masses of stable and unstable light neutrinos derive from the upper bound on the total mass density, as inferred from the lower limit $t_0>13\mathrm{}$ Gyr on the dynamical age of the Universe: If the Universe is matter dominated, $m_{\nu }<35\mathrm{} \mathrm{}\left(23\right)\mathrm{}\times max[1,{\left(\frac{t_0}{{\tau }_{\nu }}\right)}^{\frac{1}{2}}]$ eV, accordingly as a cosmological constant is (is not) allowed. The best bounds on the radiative decay of light neutrinos derive from the failure to observe prompt $\gamma$ rays accompanying the neutrinos from supernova 1987A: For any $m_{\nu }>630\mathrm{}$ eV, this provides a stronger bound on the neutrino transition moment than that obtained from red giants or white dwarfs. Our results improve on earlier cosmological and radiative decay constraints by an overall factor 20 and allow neutrinos more massive than 35 eV only if they decay overwhelmingly into singlet Majorons or other new particles with a lifetime less than one month. We review the 17-keV neutrino situation in order to stress that (1) its existence may be resolved by modest improvements in neutrino oscillation probabilities, and (2) double $\beta$ decay and nucleosynthesis constraints require that its massive partner be an active neutrino, but allow solar neutrinos to oscillate into low-mass sterile neutrinos.