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 / anti-matter 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 $(B-L)$-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 $n_B/s\simeq 4\times 10^{-12}$ can be generated from a maximally helical, right-handed (hyper)magnetic field that has a field strength of $B_0\simeq 10^{-14}\mathrm{Gauss}$ and coherence length of ${\lambda }_0\simeq 1\mathrm{pc}$ today. Relaxing an assumption that relates ${\lambda }_0$ to $B_0$, the model predicts $n_B/s\gtrsim 10^{-10}$, which could potentially explain the observed baryon asymmetry of the universe.

33 pages + 8 appendices and references, 6 figures

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