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, D, and He production; (ii) electromagnetic (EM) decay products heat the EM plasma and dilute the baryon-to-photon ratio tending to decrease He production and increase D and He production; and (iii) electron neutrinos and antineutrinos produced by tau-neutrino decays increase the weak rates that govern the neutron-to-proton ratio, leading to decreased He production for short lifetimes (< ∼ 30 sec) and masses less than about 10MeV and increased He production for long lifetimes or large masses. The precise effect of a decaying tau neutrino on the yields of primordial nucleosynthesis and the masslifetime 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., ντ → νμ + φ; φ is a very weakly interacting scalar particle); (2) sterile daughter product(s) + daughter products(s) that interacts electromagnetically (e.g., ντ → νμ+γ); (3) electron neutrino + sterile daughter product(s) (e.g., ντ → νe + φ); and (4) electron neutrino + daughter product(s) that interact electromagnetically (ντ → νe + 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 0.4MeV − 30MeV 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 30MeV, and together the two bounds very nearly exclude a long-lived tau neutrino more massive than about 0.4MeV. Further, our nucleosynthesis bounds together with other astrophysical and laboratory bounds exclude a tau neutrino of mass 0.4MeV− 30MeV 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 a tau neutrino of mass 1MeV to 10MeV and lifetime 0.1 sec − 10 sec whose decay products include an electron neutrino can reduce the He yield to less than that for two massless neutrino species. This fact could be relevant if the primordial mass fraction of He 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 (≪ 1MeV) neutrino (and other) particle species.