Neutrino-mixing-generated lepton asymmetry and the primordial ⁴He abundance

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 ⁴He yield Y resulting from this asymmetry, taking into account both the time evolution of the ν_e and ν̅ _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↔ν_s or ν_μ↔ν_s transformation which is subsequently partially converted to an asymmetry in the ν_eν̅ _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_νe≲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 ≲5% for m_νμ,ντ²-m_νs²≲10⁴ eV. We conclude that the change in the primordial ⁴He yield induced by a neutrino-mixing-generated lepton number asymmetry can be substantial in the upward direction, but limited in the downward direction.