Nucleosynthesis Limits on the Mass of Long Lived Tau and Muon Neutrinos

Abstract

We compute the nucleosynthesis bounds on the masses of stable Dirac and Majorana neutrinos by solving an evolution equation network comprising of all neutrino species which in the Dirac case includes different helicity states as separate species. We will not commit ourselves to any particular value of the nucleosynthesis bound on effective number of light neutrino degrees of freedom $N_\nu$, but present all our mass bounds as {\em functions} of $\dNu$. For example, we find that the excluded region in the mass of a Majorana $\mu$- or $\tau$- neutrino, $0.31$ MeV $< m_{\nu}^M < 52$ MeV corresponding to a bound $\dNu < 0.3$ gets relaxed to $0.93$ MeV $< m_{\nu}^M < 31$ MeV if $\dNu < 1.0$ is used instead. For the Dirac neutrinos this latter constraint gives the upper limits (for $T_{\rm QCD} = 100$ MeV): $\mnm < 0.31$ MeV and $\mnt < 0.37$ MeV. Also, the constraint $\dNu <1$ {\it allows} a stable Dirac neutrino with $m^D_{\nu_\tau} > 22$ MeV.