Primordial nucleosynthesis with a decayingτneutrino

A comprehensive study of the effect of an unstable τ neutrino on primordial nucleosyr.thesis is presented. The standard code for nucleosynthesis is modified to allow for a massive decaying τ neutrino whose daughter products include neutrinos, photons, e^± pairs, and/or noninteracting (sterile) daughter products. τ-neutrino decays influence primordial nucleosynthesis in three distinct ways: (i) the energy density of the decaying τ neutrino and its daughter products affect the expansion rate tending to increase ⁴He, D, and ³He production; (ii) electromagnetic (EM) decay products heat the EM plasma and dilute the baryon-to-photon ratio tending to decrease ⁴He production and increase D and ³He production; and (iii) electron neutrinos and antineutrinos produced by τ-neutrino decays increase the weak rates that govern the neutrino-to-proton ratio, leading to decreased ⁴He production for short lifetimes ({}30 sec) and masses less than about 10 MeV and increased ⁴He production for long lifetimes or large masses. The precise effect of a decaying τ neutrino on the yields of primordial nucleosynthesis and the mass-lifetime limits that follow depend crucially upon decay mode. We identify four generie decay modes that serve to bracket the wider range of possibilities: τ neutrino decays to (1) sterile daughter products (e.g., ν_τ→ν_μ+φ; φ is a very weakly interacting scalar particle); (2) sterile daughter product(s)+daughter products(s) that interacts electromagnetically e.g.,ν_τ→ν_μ+γ; (3) electron neutrino+sterile daughter product(s) (e.g.,ν_τ→ν_μ+φ; and (4) electron neutrino+daughter product(s) that interact electromagnetically (ν_τ→ν_μ+e^±). Mass-lifetime limits are derived for the four generic decay modes assuming that the abundance of the massive τ neutrino is determined by its electroweak annihilations. In general, nucleosynthesis excludes a τ 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 τ-neutrino mass are around 30 MeV, and together the two bounds very nearly exclude a long-lived τ neutrino more massive than about 0.4 MeV. Further, our nucleosynthesis bounds together with other astrophysical and laboratory bounds exclude a τ 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 a τ 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 ⁴He yield to less than that for two massless neutrino species. This fact could be relevant if the primordial mass fraction of ⁴He 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.