Nonconservation of lepton current and asymmetry of relic neutrinos

The neutrino asymmetry, \({n_v} - {n_{\bar v}}\), in the plasma of the early Universe generated both before and after the electroweak phase transition (EWPT) is calculated. It is well known that in the Standard Model the leptogenesis before the EWPT, in particular, for neutrinos, owes to the Abelian anomaly in a massless hypercharge field. At the same time, the generation of neutrino asymmetry in the Higgs phase after the EWPT has not been considered previously due to the absence of any quantum anomaly in an external electromagnetic field for such electroneutral particles as neutrinos, in contrast to the Adler anomaly for charged left- and right-handed massless electrons in the same electromagnetic field. Using the Boltzmann equation for neutrinos modified to include the Berry curvature term in momentum space, we establish a violation of the macroscopic neutrino current in the plasma after the EWPT and exactly reproduce the non-conservation of the lepton current in the symmetric phase before the EWPT that owes to the contribution of the triangle anomaly in an external hypercharge field but already without computing the corresponding Feynman diagrams. We apply the new kinetic equation to calculate the neutrino asymmetry by taking into account the Berry curvature and the electroweak interaction with plasma particles in the Higgs phase, including that after the neutrino decoupling in the absence of their collisions in the plasma. We find that this asymmetry is too small for observations. Thus, a difference between the relic neutrino and antineutrino densities, if it exists, must appear already in the symmetric phase of the early Universe before the EWPT.