Neutrino-Mixing-Generated Lepton Asymmetry and the Primordial $^4$He Abundance

Abstract

It has been proposed that an asymmetry in the electron neutrino sector may be generated by resonant active-sterile neutrino transformations during Big Bang Nucleosynthesis (BBN). We calculate the change in the primordial $^4$He yield $Y$ resulting from this asymmetry, taking into account both the time evolution of the $ν_e$ and $\barν_e$ distribution function and the spectral distortions in these. We calculate this change in two schemes: (1) a lepton asymmetry directly generated by $ν_e$ mixing with a lighter right-handed sterile neutrino $ν_s$; and (2) a lepton asymmetry generated by a $ν_τ\leftrightarrowν_s$ or $ν_μ\leftrightarrowν_s$ transformation which is subsequently partially converted to an asymmetry in the $ν_e\barν_e$ sector by a matter-enhanced active-active neutrino transformation. In the first scheme, we find that the percentage change in $Y$ is between -1% and 9% (with the sign depending on the sign of the asymmetry), bounded by the Majorana mass limit $m_{ν_e}\la 1$ eV. In the second scheme, the maximal percentage reduction in $Y$ is 2%, if the lepton number asymmetry in neutrinos is positive; Otherwise, the percentage increase in $Y$ is $\la 5%$ for $m^2_{ν_μ,ν_τ}-m^2_{ν_s}\la 10^4$ eV. We conclude that the change in the primordial $^4$He yield induced by a neutrino-mixing-generated lepton number asymmetry can be substantial in the upward direction, but limited in the downward direction.