PRIMORDIAL NUCLEOSYNTHESIS WITH A DECAYING TAU-NEUTRINO

A comprehensive study of the effect of an unstable tau neutrino on primordial nucleosynthesis is presented. The standard code for nucleosynthesis is modified to allow for a massive decaying tau neutrino whose daughter products include neutrinos, photons, e +/- pairs, and/or noninteracting (sterile) daughter products. tau-neutrino decays influence primordial nucleosynthesis in three distinct ways. (i) the energy density of the decaying tau neutrino and its daughter products affect the expansion rate tending to increase He-4, D, and He-3 production; (ii) electromagnetic (EM) decay products heat the EM plasma and dilute the baryon-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 the 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 of 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) + phi; phi is a very weakly interacting scalar particle); (2) sterile daughter product(s)+daughter products(s) that interacts electromagnetically (e.g., nu(tau) --> nu(mu) + gamma); (3) electron neutrino+sterile daughter product(s) (e.g., nu(tau) --> nu(e) + phi); and (4) electron neutrino + daughter product(s) that interact electromagnetically (nu(tau) --> nu(e) + e+/-). Mass-lifetime limits are derived for the four generic decay modes assuming that the abundance of the massive tau neutrino is determined by its electroweak annihilations. In general, nucleosynthesis excludes a tau neutrino of mass 0.4 MeV-30 MeV for lifetimes greater than about 300 sec. These nucleosynthesis bounds are timely since the current laboratory upper bounds to the tau-neutrino mass are around 30 MeV, and together the two bounds very nearly exclude a long-lived tau neutrino more massive than about 0.4 MeV. Further, our nucleosynthesis bounds together with other astrophysical and laboratory bounds 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 the 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 primordial 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.