PRIMORDIAL NUCLEOSYNTHESIS WITH A DECAYING TAU-NEUTRINO

A comprehensive study of the effect of an unstable tau neutrino on pri mordial nucleosynthesis is presented. The standard code for nucleosynt hesis is modified to allow for a massive decaying tau neutrino whose d aughter products include neutrinos, photons, e +/- pairs, and/or nonin teracting (sterile) daughter products. tau-neutrino decays influence p rimordial nucleosynthesis in three distinct ways. (i) the energy densi ty of the decaying tau neutrino and its daughter products affect the e xpansion rate tending to increase He-4, D, and He-3 production; (ii) e lectromagnetic (EM) decay products heat the EM plasma and dilute the b aryon-to-photon ratio tending to decrease He-4 production and increase D and He-3 production; and (iii) electron neutrinos and antineutrinos produced by tau-neutrino decays increase the weak rates that govern t he neutrino-to-proton ratio, leading to decreased He-4 production for short lifetimes (less-than-or-similar-to 30 sec) and masses less than about 10 MeV and increased He-4 production for long lifetimes or large masses. The precise effect of a decaying tau neutrino on the yields o f primordial nucleosynthesis and the mass-lifetime limits that follow depend crucially upon decay mode. We identify four generic decay modes that serve to bracket the wider range of possibilities: tau neutrino decays to (1) sterile daughter products (e.g., nu(tau) --> nu(mu) + ph i; phi is a very weakly interacting scalar particle); (2) sterile daug hter product(s)+daughter products(s) that interacts electromagneticall y (e.g., nu(tau) --> nu(mu) + gamma); (3) electron neutrino+sterile da ughter product(s) (e.g., nu(tau) --> nu(e) + phi); and (4) electron ne utrino + daughter product(s) that interact electromagnetically (nu(tau ) --> nu(e) + e+/-). Mass-lifetime limits are derived for the four gen eric decay modes assuming that the abundance of the massive tau neutri no is determined by its electroweak annihilations. In general, nucleos ynthesis excludes a tau neutrino of mass 0.4 MeV-30 MeV for lifetimes greater than about 300 sec. These nucleosynthesis bounds are timely si nce the current laboratory upper bounds to the tau-neutrino mass are a round 30 MeV, and together the two bounds very nearly exclude a long-l ived tau neutrino more massive than about 0.4 MeV. Further, our nucleo synthesis bounds together with other astrophysical and laboratory boun ds exclude a tau neutrino of mass 0.4 MeV -30 MeV of any lifetime that decays with EM daughter product(s). We use our results to constrain t he mass times relic abundance of a hypothetical, unstable species with similar decay modes. Finally, we note that tau neutrino of mass 1 MeV to 10 MeV and lifetime 0.1 sec-10 sec whose decay products include an electron neutrino can reduce the He-4 yield to less than that for two massless neutrino species. This fact could be relevant if the primord ial mass fraction of He-4 is found to be less than about 0.23 and can also lead to a modification of the nucleosynthesis bound to the number of light (<< 1 MeV) neutrino (and other) particle species.