BIG-BANG NUCLEOSYNTHESIS CONSTRAINTS ON THE TAU-NEUTRINO MASS

We re-examine the effect of a massive tau neutrino on primordial nucleosynthesis. An improved calculation of the evolution of the total energy density is presented for both a stable tau neutrino, and for the case where the tau neutrino decays into a lighter neutrino and a scalar. The production of light elements in big bang nucleosynthesis is calculated for the stable tau neutrino and for the unstable case. Using observational limits on the abundances of He-4, D + He-3, and Li-7, we constrain the allowed mass and lifetime of nu(tau). We find that the only range allowed for the mass and lifetime is either m(nu)tau less-than-or-similar-to 0.1 MeV for tau(nu) greater-than-or-similar-to 10(-2) s and m(nu)tau less-than-or-similar-to 0.1 (tau(nu)/10(-2) s) MeV for tau(nu) less-than-or-similar-to 10(-2) s, or 5-10 MeV less-than-or-similar-to m(nu)tau less-than-or-equal-to 31 MeV provided that tau(nu) less-than-or-similar-to 40 s, where we use the experimental upper bound on m(nu)tau from tau --> 5pi(+/-)nu(tau). Tau neutrinos with lifetimes longer than 40 s are excluded by BBN in the mass interval 0.1 MeV less-than-or-similar-to m(nu)tau less-than-or-similar-to 50 MeV.