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Neutrino Masses

In the big-bang scenario of the early universe one expects about as many ``blackbody neutrinos'' as the measured density of cosmic microwave photons. In units of the critical density one infers a neutrino cosmic energy density of $\Omega_\nu h^2=\sum_{i=1}^3m_i/93\,{\rm eV}$, where h is the Hubble constant in units of $100\,\rm km\,s^{-1}\,Mpc^{-1}$. The observed age of the universe together with the measured expansion rate yields $\Omega h^2\leq0.5$ so that
 \begin{displaymath}m_\nu\leq 50\,{\rm eV}\end{displaymath} (1.5)
 

for any flavour. If one of the neutrinos had a mass near this bound it would provide a significant fraction of the cosmic dark matter. Theories of cosmological structure formation disfavour ``hot dark matter'' (e.g. neutrinos). However, ``cold dark matter'' (e.g. neutralinos) overproduce structure on small scales, a problem that can be patched up in a ``mixed dark matter'' scenario with $\sum_{i=1}^3m_i=5\,{\rm eV}$. Even a ``sub-critical'' neutrino mass is cosmologically interesting! Besides relying on the standard big-bang picture, Eq. ([*]) depends on the assumption that neutrinos do not decay fast on cosmological time scales. The dominant standard-model decays of mixed neutrinos are $\nu\to\nu'\gamma$ or $\nu\to\nu'\gamma\gamma$ which are far too slow to invalidate Eq. ([*]). In addition, radiative decays have been constrained from the absence of anomalous cosmic photon backgrounds in various energy bands. The experimental $\nu_\tau$ mass limit exceeds 2me so that $\nu_\tau\to\nu_e e^+e^-$ is possible, and could be fast enough to invalidate Eq. ([*]). However, $\gamma$ rays for the inner Bremsstrahlung process $\nu_\tau\to\nu_e e^+e^-\gamma$ have not been observed by the SMM or COMPTEL satellites from SN 1987A, providing very restrictive limits on this process. One infers that all three sequential neutrinos must obey Eq. ([*]) unless they decay fast into ``invisible'' channels by non-standard couplings. Turning this around, experimental searches for neutrinos with masses exceeding Eq. ([*]) are tantamount to searching for novel neutrino couplings beyond the standard model. The $\bar\nu_e$ signal duration of SN 1987A yields a limit on dispersion effects. In particular

\begin{displaymath}m_{\nu_e}\leq 20\,\rm eV,\end{displaymath} (1.6)
 

somewhat less restrictive than the corresponding laboratory limits from tritium $\beta$ decay. The best direct mass limits could be obtained from a future galactic SN if the neutrino signal is measured in a detector like Superkamiokande in conjunction with the proposed Supernova Burst Observatory (SNBO). Optimistically, one may be able to achieve a sensitivity down to the 10 eV range even for $\nu_\mu$ and $\nu_\tau$


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