BIG-BANG NUCLEOSYNTHESIS CONSTRAINTS ON THE TAU-NEUTRINO MASS

We re-examine the effect of a massive tau neutrino on primordial nucle osynthesis. An improved calculation of the evolution of the total ener gy density is presented for both a stable tau neutrino, and for the ca se where the tau neutrino decays into a lighter neutrino and a scalar. The production of light elements in big bang nucleosynthesis is calcu lated for the stable tau neutrino and for the unstable case. Using obs ervational limits on the abundances of He-4, D + He-3, and Li-7, we co nstrain the allowed mass and lifetime of nu(tau). We find that the onl y 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 t au(nu) less-than-or-similar-to 10(-2) s, or 5-10 MeV less-than-or-simi lar-to m(nu)tau less-than-or-equal-to 31 MeV provided that tau(nu) les s-than-or-similar-to 40 s, where we use the experimental upper bound o n 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.