Constraints from primordial nucleosynthesis on the mass of the τ neutrino

The familiar nucleosynthesis constraint on the number of neutrino species, N_ν{≤}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 τ_ν{}1 sec, and from 0.3 to 30 MeV (Dirac) and 0.5 to 32 MeV (Majorana) for τ_ν{}10³ 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 τ_ν{}1 sec).