Can We Rule Out a Heavy Tau Neutrino?

Recent experimental results give an upper bound of 164 MeV for the tau neutrino mass. By combination of experimental limits on neutrino mixing angles with constraints on the destruction of deuterium after nucleosynthesis it is possible to raise our previous lower bound of 23 MeV to 50 MeV, and modulo recent less certain results, to 120 MeV. If data on mixing angles improve by several orders of magnitude it should be possible to rule out completely a heavy [$>O\left(1\mathrm{} \mathrm{MeV}\right)$] tau neutrino mass.