Primordial nucleosynthesis with a decayingτneutrino

A comprehensive study of the effect of an unstable $\tau$ neutrino on primordial nucleosyr.thesis is presented. The standard code for nucleosynthesis is modified to allow for a massive decaying $\tau$ neutrino whose daughter products include neutrinos, photons, $e^{\pm }$ 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 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, D, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ production; (ii) electromagnetic (EM) decay products heat the EM plasma and dilute the baryon-to-photon ratio tending to decrease ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ production and increase D and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ 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 ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ production for short lifetimes (≲30 sec) and masses less than about 10 MeV and increased ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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 generie decay modes that serve to bracket the wider range of possibilities: $\tau$ neutrino decays to (1) sterile daughter products (e.g., ${\nu }_{\tau }\to {\nu }_{\mu }+\phi$; $\phi$ is a very weakly interacting scalar particle); (2) sterile daughter product(s)+daughter products(s) that interacts electromagnetically e.g.,${\nu }_{\tau }\to {\nu }_{\mu }+\gamma$; (3) electron neutrino+sterile daughter product(s) (e.g.,${\nu }_{\tau }\to {\nu }_{\mu }+\phi$; and (4) electron neutrino+daughter product(s) that interact electromagnetically (${\nu }_{\tau }\to {\nu }_{\mu }+e^{\pm }$). 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