Nucleosynthesis and the Mass of theτNeutrino

The primordial abundance of long-lived heavy Majorana neutrinos is calculated from the full Boltzmann equation. Inclusion of scattering reactions drastically changes the predicted abundance of a heavy neutrino species. This loosens the well known mass constraint on MeV neutrinos from big bang nucleosynthesis, and allows for the existence of a Majorana $\tau$ neutrino with mass $m_{{\nu }_{\tau }}\ge 11\mathrm{MeV}$. Further experimental efforts are therefore needed to investigate the range $11\le m_{{\nu }_{\tau }}\le 24\mathrm{MeV}$. Some interesting cosmological consequences of an MeV ${\nu }_{\tau }$ are also pointed out.