Hypermagnetic helicity evolution in early universe: leptogenesis and
  hypermagnetic diffusion
  We study hypermagnetic helicity and lepton asymmetry evolution in plasma of
the early Universe before the electroweak phase transition (EWPT) accounting
for chirality flip processes via inverse Higgs decays and sphaleron transitions
which violate the left lepton number and wash out the baryon asymmetry of the
Universe (BAU). In the scenario where the right electron asymmetry supports the
BAU alone through the conservation law $B/3 - L_{eR}=const$ at temperatures
$T>T_{RL}\simeq 10 TeV$ the following universe cooling leads to the production
of a non-zero left lepton (electrons and neutrinos) asymmetry. This is due to
the Higgs decays becoming more faster when entering the equilibrium at
$T=T_{RL}$ with the universe expansion, $\Gamma_{RL}\sim T> H\sim T^2$,
resulting in the parallel evolution of both the right and the left electron
asymmetries at $T<T_{RL}$ through the corresponding Abelian anomalies in SM in
the presence of a seed hypermagnetic field. The hypermagnetic helicity
evolution proceeds in a self-consistent way with the lepton asymmetry growth.
The role of sphaleron transitions decreasing the left lepton number turns out
to be negligible in given scenario. The hypermagnetic helicity can be a supply
for the magnetic one in Higgs phase assuming a strong seed hypermagnetic field
in symmetric phase.
