Baryogenesis via the Chiral Magnetic Effect in a First-Order Electroweak Phase Transition

TL;DR

The paper investigates baryogenesis during a first-order electroweak phase transition within the Standard Model extended by dimension-six CP-violating operators, focusing on the generation and evolution of helical hypermagnetic fields and their connection to the BAU via the chiral anomaly. It shows that without the chiral magnetic effect (CME) the produced BAU from hypermagnetic helicity is too small to explain observations, particularly under current EDM constraints on the CP-violating operator. Incorporating CME, the authors demonstrate that plausible EWPT parameters can yield the observed BAU with initial field strengths $B_0$ in the range $[10^{-7},10^{-3}] m_W^2$ and a wide range of transition dynamics, linking microphysical CP violation to macroscopic magnetic-field evolution. The study provides a concrete framework tying SMEFT CP violation, CME, and primordial magnetic fields to BAU, while noting that the resulting fully helical fields are unlikely to be detectable with current observations. Overall, the work highlights a viable CME-assisted baryogenesis mechanism during the EWPT and clarifies the observational and EFT-viability implications of this scenario.

Abstract

In this paper, we investigate the generation of the baryon asymmetry of the universe during the first-order electroweak phase transition. We first study the generation of the helical magnetic field in the framework of the standard model effective field theory with a CP-violating operator. We show that, when the chiral magnetic effect is absent, the helical magnetic field and effective chemical potential cannot generate enough baryon asymmetry when vacuum bubbles collide. We further find that the chiral magnetic effect can amplify the lepton asymmetry in the early universe during the phase transition. We present the baryon asymmetry interpretation requirement on certain parameter spaces of the phase transition and the primordial magnetic field.

Figures (8)

• Figure 1: Left: The scalar field of two colliding bubbles in the case of $t_{col}m_{\rm w}=200$; Right: The Higgs phase $\Theta$ is the field is shown as a The function of distance z along the axis of collision for $\tau m_{\rm w}=160,180,200,220$, with $\Theta_0=1$.
• Figure 2: Left: The strength of the MFs as a function of the distance $z$ along the axis of collision at different times when $v_{\rm w}=0.7,~l_{\rm w}=0.025,~\Lambda=600$ GeV. Right: The strength of the MFs at $\tau m_{\rm w}=160$ for $\Lambda =600$ GeV, $v_{\rm w}=0.33,~l_{\rm w}=0.048$ for $\Lambda =700$ GeV, $v_{\rm w}=0.14,~l_{\rm w}=0.11$ for $\Lambda =800$ GeV, $v_{\rm w}=0.07,~l_{\rm w}=0.19$ for $\Lambda =900$ GeV.
• Figure 3: The bubble wall velocity and the phase transition duration for different NP scales.
• Figure 4: Left: $h_Y$ as a function of the new physics scale $\Lambda$. Right: $h_Y$ as a function of the effective hypercharge chemical potential $\mu_{eff}^Y$. In both panels, the curves correspond to $\tau m_{\mathrm{w}}=160, 180, 200$, as indicated in the legend.
• Figure 5: Dependence of the baryon-to-entropy ratio $\eta_B$ on the NP scale $\Lambda$ for different values of the dimensionless bubble-wall collision times $\tau m_w = 160,\,180,\,200$. The points correspond to $\Lambda = 600,\,700,\,800,\,900~\mathrm{GeV}$.