Generation of hypermagnetic helicity and leptogenesis in early universe
  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 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 plays a key role
in lepto/baryogenesis in our scenario and the more hypermagnetic field is close
to the maximum helical one the faster BAU grows up the observable value ,
$B_{obs}\sim 10^{-10}$.
