Baryogenesis from decaying magnetic helicity

Abstract

As a result of the Standard Model chiral anomalies, baryon number is violated in the early Universe in the presence of a hypermagnetic field with varying helicity. We investigate whether the matter/antimatter asymmetry of the Universe can be created from the decaying helicity of a primordial (hyper)magnetic field before and after the electroweak phase transition. In this model, baryogenesis occurs without ($B\ensuremath{-}L$)-violation, since the ($B+L$) asymmetry generated by the hypermagnetic field counteracts the washout by electroweak sphalerons. At the electroweak crossover, the hypermagnetic field becomes an electromagnetic field, which does not source ($B+L$). Although the sphalerons remain in equilibrium for a time, washout is avoided since the decaying magnetic helicity sources chirality. The relic baryon asymmetry is fixed when the electroweak sphaleron freezes out. Under reasonable assumptions, a baryon asymmetry of ${n}_{B}/s\ensuremath{\simeq}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ can be generated from a maximally helical, right-handed (hyper)magnetic field that has a field strength of ${B}_{0}\ensuremath{\simeq}{10}^{\ensuremath{-}14}\text{ }\text{ }\text{Gauss}$ and coherence length of ${\ensuremath{\lambda}}_{0}\ensuremath{\simeq}1\text{ }\text{ }\mathrm{pc}$ today. Relaxing an assumption that relates ${\ensuremath{\lambda}}_{0}$ to ${B}_{0}$, the model predicts ${n}_{B}/s\ensuremath{\gtrsim}{10}^{\ensuremath{-}10}$, which could potentially explain the observed baryon asymmetry of the Universe.