Nonconservation of lepton current and asymmetry of relic neutrinos

Abstract

The neutrino asymmetry in the early universe plasma, $n_\nu - n_{\bar \nu}$, is calculated both before and after the electroweak phase transition (EWPT). The leptogenesis before EWPT within the standard model is well known to be driven by the abelian anomaly in a massless hypercharge field. The generation of the neutrino asymmetry in the Higgs phase after EWPT, in its turn, has not been considered previously because of the absence of any quantum anomaly in an external electromagnetic field for such electroneutral particles as neutrino, unlike the Adler anomaly for charged left and right polarized massless electrons in the same electromagnetic field. Using the neutrino Boltzmann equation, modified by the Berry curvature term in the momentum space, we establish the violation of the macroscopic neutrino current in plasma after EWPT and exactly reproduce the nonconservation of the lepton current in the symmetric phase before EWPT arising in quantum field theory due to the non-zero lepton hypercharge and corresponding triangle anomaly in an external hypercharge field. In the last case the violation of the lepton current is derived through the kinetic approach without the computation of the corresponding Feynman diagrams. Then the new kinetic equation is applied for the calculation of the neutrino asymmetry accounting for the the Berry curvature and the electroweak interaction with background fermions in the Higgs phase, including the stage after the neutrino decoupling at the absence of neutrino collisions in plasma. This asymmetry is found to be rather small to be observed. Thus, a difference of the relic neutrino and antineutrino densities, if exists, should be acquired mainly in the symmetric phase before EWPT.