Lepton asymmetry growth in the symmetric phase of an electroweak plasma
  with hypermagnetic fields versus its washing out by sphalerons
  We study lepton asymmetry evolution in plasma of the early Universe before
the electroweak phase transition (EWPT) accounting for chirality flip processes
via Higgs decays (inverse decays) entering equilibrium at temperatures below
T_RL ~ 10 TeV, T_EW < T < T_RL. We solve appropriate kinetic equations for
leptons and Higgs bosons taking into account the lepton number violation due to
Abelian anomalies for right and left electrons and neutrinos in the
self-consistent hypercharge field obeying Maxwell equations modified by the
contribution of the Standard Model of electroweak interactions. The violation
of left lepton numbers and the corresponding violation of the baryon number due
to sphaleron processes in symmetric phase is taken into account as well.
Assuming the Chern-Simons wave configuration of the seed hypercharge field, we
get the estimates of baryon and lepton asymmetries evolved from the primordial
right electron asymmetry existing alone as partial asymmetry at T > T_RL. One
finds a strong dependence of the asymmetries on the Chern-Simons wave number.
We predict a nonzero chiral asymmetry \Delta \mu = \mu_e_R - \mu_e_L \neq 0 in
this scenario evolved down to the EWPT moment that can be used as an initial
value for the Maxwellian field evolution after EWPT.
