The generation of baryon asymmetry and hypermagnetic field by the chiral vortical effect in the presence of sphalerons
We show how the temperature-dependent chiral vortical effect can generate hypermagnetic fields and matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range $100\mbox{GeV} \le T\le 10\mbox{TeV}$, even in the presence of the weak sphaleron processes. We take into account all perturbative chirality-flip processes, as well as the nonperturbative Abelian and non-Abelian anomalous effects for all three generations. Using the constraints and conservation laws in the plasma, we reduce the number of required evolution equations. We also simplify the anomalous transport coefficients, accordingly. We consider both monochromatic and continuous spectra for the hypermagnetic and velocity fields to solve the anomalous magnetohydrodynamics equations. We then show that overlapping small transient fluctuations in the temperature of some matter degrees of freedom and vorticity of the plasma can generate a chiral vortical current, resulting in the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We obtain the baryon asymmetry $\eta_{B}\simeq 5\times10^{-10}$ and a positive helicity hypermagnetic field with amplitude $B_{Y}(x)\simeq10^{19}G$, at the onset of the electroweak phase transition. Although the sphaleron processes tend to washout the generated $(\rm B +L)$ asymmetry, the anomalous processes prevail and the baryogenesis and leptogenesis occur without $(\rm B-L)$ violation.