Generation of the relic neutrino asymmetry in a hot plasma of the early
  Universe
  The neutrino asymmetry in the early universe plasma, $n_\nu - n_{\bar \nu}$,
is calculated both before and after the electroweak phase transition (EWPT). In
the Standard Model before EWPT, the leptogenesis 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-Bell-Jackiw 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 nonzero
lepton hypercharge and corresponding triangle anomaly in an external
hypercharge field. In the last case, the non-conservation of the lepton current
is derived through the kinetic approach without a computation of corresponding
Feynman diagrams. Then the new kinetic equation is applied for the calculation
of the neutrino asymmetry accounting for the Berry curvature and the
electroweak interaction with background fermions in the Higgs phase. Such an
interaction generates a neutrino asymmetry through the electroweak coupling of
neutrino currents with electromagnetic fields in plasma, which is $\sim
G_\mathrm{F}^2$. It turns out that this effect is especially efficient for
maximally helical magnetic fields.
