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 (hB) and the Chern-Simons numbers of the non-Abelian gauge fields (NCS,w and NCS,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 hB and NCS,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 hB and NCS,w, the existence of which had been inferred earlier. In particular we show that, in the scenario that we study, an initial hB decays mostly to NCS,w, with only 10−3 conversion ratio into B+L asymmetry.