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 ${\nu }_e$ and ${\bar{\nu }}_e$ distribution function and the spectral distortions in these. We calculate this change in two schemes: (1) a lepton asymmetry directly generated by ${\nu }_e$ mixing with a lighter right-handed sterile neutrino ${\nu }_s$; and (2) a lepton asymmetry generated by a ${\nu }_{\tau }\leftrightarrow {\nu }_s$ or ${\nu }_{\mu }\leftrightarrow {\nu }_s$ transformation which is subsequently partially converted to an asymmetry in the ${\nu }_e{\bar{\nu }}_e$ 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.

15 pages, 7 figures, submitted to PRD

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