Massive Decaying Tau Neutrino and Big Bang Nucleosynthesis

Comparing Big Bang Nucleosynthesis predictions with the light element abundances inferred from observational data, we can obtain the strong constraints on some neutrino properties, e.g. number of neutrino species, mass, lifetime. Recently the deuterium abundances were measured in high red-shift QSO absorption systems. It is expected that they are close to the primordial values, however, two groups have reported inconsistent values which are different in one order of magnitude. In this paper we show how we can constrain on $\tau$ neutrino mass and its lifetime in each case when we adopt either high or low deuterium data. We find that if $0.01 \sec \lesssim \tau_{\nutau} \lesssim 1 \sec$ and $10\mev \lesssim m_{\nutau} \lesssim 24\mev$, the theoretical predictions agree with the low D/H abundances. On the other hand if we adopt the high D/H abundances, we obtain the upper bound of $\tau$ neutrino mass, $m_{\nutau}\lesssim 20 \mev$.