Bounds on Dirac Neutrino Masses from Nucleosynthesis

We derive new bounds on the Dirac mass of the tau and muonic neutrinos. By solving the kinetic equation for the rate of energy deposition due to helicity flipping processes and imposing the constraint that the number of effective species contributing to the energy density at the time of nucleosynthesis be $\Delta k_\nu<~0.3$, we find the bounds $m_{\nu_\mu} < ~150$ KeV and $m_{\nu_\tau} < ~190$ KeV for $T_{\rm QCD}= 200$ MeV. The constraint $\Delta k_\nu~<0.1~$ leads to the much stronger bound $m_\nu <10$ KeV for both species of neutrinos.