Global charge conservation in the symmetric phase of the early Universe

In the Standard Model at high temperatures, anomalous effects contribute to the violation of baryon number ( B ) and lepton number ( L ), separately, while B − L remains conserved. There are also corresponding changes in the helicity of the hypermagnetic field ( h B ) and the Chern-Simons numbers of the non-Abelian gauge fields ( N CS,w and N CS,s ). In this study, we investigate a baryogenesis process in the symmetric phase of the early Universe by taking into account the Abelian and non-Abelian anomalous effects as well as the perturbative chirality-flip processes of all fermions. We calculate the time evolution of all relevant physical quantities, including the asymmetries of all fermions and the Higgs, as well as h B and N CS,w . We present a method to compute the latter, for which it is crucial to consider the minute departure from equilibrium of the sphaleron processes. We then verify explicitly the conservation of a global charge, involving the total matter-antimatter asymmetry B + L , the hypermagnetic helicity h B and N CS,w , the existence of which had been inferred earlier. In particular we show that, in the scenario that we study, an initial h B decays mostly to N CS,w , with only 10 − 3 conversion ratio into B + L asymmetry.