Big Bang Nucleosynthesis and Active-Sterile Neutrino Mixing: Evidence for Maximal Mu Neutrino <-> Tau Neutrino Mixing in Super Kamiokande?

Abstract

We discuss Big Bang Nucleosynthesis constraints on maximal $ν_μ\leftrightarrowν_s$ mixing. Vacuum $ν_μ\leftrightarrowν_s$ oscillation has been proposed as one possible explanation of the Super Kamiokande atmospheric neutrino data. Based on the most recent primordial abundance measurements, we find that the effective number of neutrino species for Big Bang Nucleosynthesis (BBN) is $N_ν\la 3.3$. Assuming that all three active neutrinos are light (with masses $\ll 1$ MeV), we examine BBN constraints on $ν_μ\leftrightarrowν_s$ mixing in two scenarios: (1) a negligible lepton asymmetry (the standard picture); (2) the presence of a large lepton asymmetry which has resulted from an amplification by $ν_τ\leftrightarrowν_{s'}$ mixing ($ν_{s'}$ being $ν_s$ or another sterile neutrino species). The latter scenario has been proposed recently to reconcile the BBN constraints and large-angle $ν_μ\leftrightarrowν_s$ mixing. We find that the large-angle $ν_μ\leftrightarrowν_s$ mixing in the first scenario, which would yield $N_ν\approx 4$, is ruled out as an explanation of the Super Kamiokande data. It is conceivably possible for the $ν_μ\leftrightarrowν_s$ solution to evade BBN bounds in the second scenario, but only if 200 eV$^2\la m^2_{ν_τ}-m^2_{ν_{s'}}\la 10^4$ eV$^2$ is satisfied, and if $ν_τ$ decays non-radiatively with a lifetime $\la 10^3$ years. This mass-squared difference implies 15 eV$\la m_{ν_τ}\la 100$ eV if $ν_{s'}$ is much lighter than $ν_τ$. We conclude that maximal (or near maximal) $ν_μ\leftrightarrowν_τ$ mixing is a more likely explanation of the Super Kamiokande data.