Electron-, mu-, and tau-number conservation in a supernova core

We study if the neutrino mixing parameters suggested by the atmospheric neutrino anomaly imply chemical equilibrium between μ- and τ-flavored leptons in a supernova (SN) core. The initial flavor-conversion rate would indeed be fast if the ν_μ-ν_τ-mixing angle were not suppressed by second-order refractive effects. The neutrino diffusion coefficients are different for ν_μ, ν_μ, ν_τ, and ν_τ so that neutrino transport will create a net μ and τ lepton number density. This will typically lead to a situation where the usual first-order refractive effects dominate, further suppressing the rate of flavor conversion. Altogether, neutrino refraction has the nontrivial consequence of guaranteeing the separate conservation of e, μ, and τ lepton number in a SN core on the infall and cooling time scales, even when neutrino mixing angles are large.