Chiral magnetic effect amplified baryogenesis at first-order phase transitions

In this study, we show that, in the background of the primordial magnetic field, the chiral magnetic effect effect can significantly amplify the chiral chemical potential sourced by the CP violation near the bubble walls during the first-order electroweak phase transition. This effect can lift the generated baryon asymmetry by several orders, and make it possible to explain the baryon asymmetry of the Universe with a CPV in the fermion sector far beyond the limitation of the electron dipole moment.

💡 Research Summary

In this work the authors investigate how a primordial hypermagnetic field can dramatically boost electroweak baryogenesis (EWBG) through the chiral magnetic effect (CME). The setting is a first‑order electroweak phase transition (EWPT) in which expanding bubbles of broken‑phase Higgs vacuum nucleate and sweep through the symmetric plasma. Near the bubble wall a CP‑violating (CPV) source is introduced in the τ‑lepton sector via a dimension‑six operator (Λ_f⁻²) that gives the τ mass a complex phase proportional to iγ₅. The CPV source term, S_CP∝y_τ²ϕ_b³ϕ’_b/Λ_f², is sharply localized at the wall because it depends on the third power of the Higgs profile and its derivative.

The CPV source generates a chiral (axial) chemical potential μ₅ for the τ‑leptons. The evolution of μ₅ in the symmetric phase is governed by a diffusion‑advection‑damping equation that also contains the anomalous term α E·B, where E and B are the hyper‑electric and hyper‑magnetic fields. The key novelty is that μ₅ feeds back into the magnetohydrodynamic (MHD) equations via the CME term ∇×(μ₅ B). In the planar‑wall approximation the coupled set of equations reduces to three one‑dimensional PDEs for μ₅, B_x and B_y. The hyper‑conductivity σ≈70 T, the chiral conductivity α_Y≈g’^2/(4π)≈0.01, and the diffusion constant D_eff are all taken from standard electroweak plasma physics.

The authors solve these equations numerically with realistic parameters: bubble wall velocity v_w≈0.05, wall thickness L_w≈0.11 GeV⁻¹, nucleation temperature T_n≈88 GeV, and an initial homogeneous hypermagnetic field B₀≈10⁻³ GeV² (corresponding today to ≈7×10⁻¹⁸ G). The simulation shows a rapid build‑up of μ₅ at the wall, which then induces a localized distortion of the transverse magnetic field through the CME term. This distortion grows exponentially for a short period, amplifying B by up to two orders of magnitude. The amplified B, in turn, enhances the α E·B term, feeding back into μ₅ and creating a positive feedback loop that quickly reaches a quasi‑steady profile.

The chiral chemical potential then sources the baryon chemical potential μ_B via the weak sphaleron rate Γ_ws. Solving the diffusion‑advection equation for μ_B yields a baryon‑to‑entropy ratio η_B that is 10²–10³ times larger than the standard EWBG prediction (which scales as η_B∝Λ_f⁻²). The enhancement is most pronounced for small wall velocities and thin walls, because the CPV source remains active longer and is more sharply localized, allowing μ₅ to grow larger before advection sweeps it away. Conversely, fast walls suppress the CPV source but the CME‑induced magnetic amplification partially compensates.

A systematic scan of the cutoff scale Λ_f shows that, unlike the conventional scenario where η_B falls off as Λ_f⁻², the CME‑driven mechanism weakens this dependence dramatically. Even for Λ_f≈1 TeV, where EDM constraints would normally forbid sufficient CP violation, the feedback loop can still generate the observed η_B≈8×10⁻¹¹. The authors also explore the dependence on the phase‑transition time scale Δt_pt∝(β/H)⁻¹. For very rapid transitions (β/H≳10⁵ at T≈100 GeV) the CME does not have enough time to act, and the enhancement disappears. This sets a clear phenomenological bound on the viable parameter space.

In the concluding discussion the authors emphasize that a consistent treatment of anomalous transport and MHD dynamics is essential for any realistic first‑order EWPT model. The CME provides a natural way to reconcile successful baryogenesis with stringent electric‑dipole‑moment limits, opening new regions of model space that were previously excluded. They suggest that future work should incorporate the generation mechanism of the primordial magnetic field, its possible helicity, and the back‑reaction on the bubble dynamics, as well as a more detailed treatment of turbulence and non‑linear MHD effects.

Overall, the paper presents a compelling case that primordial hypermagnetic fields, through the chiral magnetic effect, can act as a catalyst for electroweak baryogenesis, substantially relaxing the need for large CP‑violating phases and offering a fresh avenue for model building in the quest to explain the matter‑antimatter asymmetry of the Universe.