Nucleosynthesis limits on the mass of long lived tau and muon neutrinos

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 the effective number of light neutrino degrees of freedom N_v, but present all our mass bounds as functions of ΔN_v. For example, we find that the excluded region in the mass of a Majorana μ- or τ-neutrino, 0.29 MeV < m^M_v < 53 MeV corresponding to a bound ΔN_v < 0.3 gets relaxed to 0.95 MeV < m^M_v < 32 MeV if ΔN_v < 1.0 is used instead. For the Dirac neutrinos ΔN_v < 1.0 gives the upper limits (for T_QCD = 100 MeV) m^D_vμ < 0.31 MeV and m^D_v- < 0.37 MeV and the lower limit m^D_v > 25 MeV. Together with the present experimental limit nucleosynthesis excludes m^M_vτ > 0.95 MeV and m^D_vτ > 0.37 MeV at 95% CL.