Leptogenesis via hypermagnetic fields and baryon asymmetry

We study baryon asymmetry generation originated from the leptogenesis in the presence of hypermagnetic fields in the early Universe plasma before the electroweak phase transition (EWPT). For the simplest Chern-Simons (CS) wave configuration of hypermagnetic field we find the baryon asymmetry growth when the hypermagnetic field value changes due to alpha^2-dynamo and the lepton asymmetry rises due to the Abelian anomaly. We solve the corresponding integro-differential equations for the lepton asymmetries describing such self-consistent dynamics for lepto- and baryogenesis in the two scenarios : (i) when a primordial lepton asymmetry sits in right electrons e_R; and (ii) when, in addition to e_R, a left lepton asymmetry for e_L and nu_eL arises due to chirality flip reactions provided by inverse Higgs decays at the temperatures, T<T_RL ~ 10 TeV. We find that the baryon asymmetry of the Universe (BAU) rises very fast through such leptogenesis, especially, in strong hypermagnetic fields. Varying (decreasing) the CS wave number parameter k_0 < 10^-7 T_EW one can recover the observable value of BAU, eta_B ~ 10^-9, where k_0 = 10^-7 T_EW corresponds to the maximum value for CS wave number surviving ohmic dissipation of hypermagnetic field. In the scenario (ii) one predicts the essential difference of the lepton numbers of right - and left electrons at EWPT time, L_eR - L_eL ~ (mu_eR - mu_eL) / T_EW = Delta mu / T_EW ~ 10^-5 that can be used as an initial condition for chiral asymmetry after EWPT.