Chiral magnetic effect amplified baryogenesis at first-order phase transitions

TL;DR

Problem: achieving the observed BAU within EWBG without conflicting EDM constraints is challenging. Approach: incorporate CME-driven MHD feedback in a planar-wall tau-CPV EWPT scenario, solving transport and magnetic evolution to obtain mu5, B, and muB. Contributions: shows CME amplifies magnetic helicity, enhances lepton chiral asymmetry, and boosts BAU by orders of magnitude, weakening the eta_B propto 1/Lambda_f^2 scaling; identifies viable regions with moderate phase-transition temperatures and inverse durations, and discusses gravitational-wave implications. Significance: opens new parameter space for BAU explanations and demonstrates the dynamical role of primordial magnetic fields in baryogenesis.

Abstract

In this study, we show that, in the background of the primordial magnetic field, the CME 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.

Figures (4)

• Figure 1: Time evolution of the chiral chemical potential and magnetic field near the electroweak bubble wall. Upper: Spatial profiles of the chiral chemical potential $\mu_5(t,z)$, generated by the CPV $\tau$-sector source localized on the bubble wall. Lower: Corresponding evolution of the transverse local hypermagnetic field magnitude ${B}(t,z)=\sqrt{B_x^2(t,z)+B_y^2(t,z)}$ including the CME near the wall in the symmetry phase. Results are shown for several representative times $t=0,10,30,50\;\mathrm{GeV}^{-1}$ with the wall centered at $z=0$.
• Figure 2: Bubble wall velocity dependence of the baryon asymmetry in CME amplified electroweak baryogenesis, the y/x-axis is plotted on a base-10 logarithmic scale. The three color-matched pairs of curves correspond to snapshots at $t=10, 30, 50,\; \mathrm{GeV^{-1}}$. Solid (dashed) curves use a thick (thin) wall profile with $L_w=0.11\;\mathrm{GeV^{-1}} (L_w=0.011\; \mathrm{GeV^{-1}})$. The CPV source is generated in the $\tau$-sector with a cutoff $\Lambda_f=1000\;\mathrm{GeV}$, and the baryon number is sourced through the weak sphaleron response to $\mu_5$ encoded in the $\mu_B$ equation.
• Figure 3: Dependence of the baryon asymmetry on the cutoff scale $\Lambda_f$. Solid curves correspond to the baryon asymmetry ($\eta_B=n_B/s$) obtained from numerically solving Eqs. (\ref{['eq:mu5-final']},\ref{['eq:Bxfinal9']},\ref{['eq:Byfinal10']},\ref{['eq:muB-final11']}). The final evolutionary outcome is that over a long period of time $t=800~\mathrm{GeV}^{-1}$, all situations reach a saturation point. Dashed curves show the standard EWBG prediction computed from the semi-analytic expression of Eq. \ref{['YB1811']}. The black horizontal line represents the observed value of the baryon asymmetry $(8.2-9.4)\times10^{-11}$ParticleDataGroup:2018ovx.
• Figure 4: Bubble expansion time $\Delta t_{pt}$ as a function of phase transition inverse duration $\beta/H$ for representative temperatures $T_{\star}=1, 10^2, 10^4\;\mathrm{TeV}$. The curves are obtained from $\Delta t_{pt}=[(\beta/H)H(T)]^{-1}$ with the radiation dominated expansion rate $H(T)$. The gray region is the parameter space used to evolve the magnetic field and chemical potential equations.