Constraints from primordial nucleosynthesis on the mass of the τ neutrino

The familiar nucleosynthesis constraint on the number of neutrino species, ${\mathit{N}}_{\nu }$≤3.4, applies to massless neutrino species. An MeV-mass neutrino can have even greater impact, and we show that primordial nucleosynthesis excludes a τ-neutrino mass from 0.3 to 25 MeV (Dirac) and 0.5 to 25 MeV (Majorana) provided that its lifetime ${\mathrm{\tau }}_{\nu }$≳1 sec, and from 0.3 to 30 MeV (Dirac) and 0.5 to 32 MeV (Majorana) for ${\mathrm{\tau }}_{\nu }$≳${10}^3$ sec. A modest improvement in the laboratory mass limit—from 35 to 25 MeV—would imply that the τ-neutrino mass must be less than 0.5 MeV (provided ${\mathrm{\tau }}_{\nu }$≳1 sec).