CONSTRAINTS FROM PRIMORDIAL NUCLEOSYNTHESIS ON THE MASS OF THE TAU NEUTRINO

The familiar nucleosynthesis constraint on the number of neutrino species, N(v) less-than-or-equal-to 3.4, applies to massless neutrino species. An MeV-mass neutrino can have even greater impact, and we show that primordial nucleosynthesis excludes a tau-neutrino mass from 0.3 to 25 MeV (Dirac) and 0.5 to 25 MeV (Majorana) provided that its lifetime tau-v greater-than-or-similar-to sec, and from 0.3 to 30 MeV (Dirac) and 0.5 to 32 MeV (Majorana) for tau-v greater-than-or-similar-to 10(3) sec. A modest improvement in the laboratory mass limit - from 35 to 25 MeV - would imply that the tau-neutrino mass must be less than 0.5 MeV (provided tau-v greater-than-or-similar-to 1 sec).