Resonant Flavor Oscillations in Electroweak Baryogenesis

TL;DR

This work develops a consistent framework for electroweak baryogenesis transport by formulating a power-counting scheme in ratios of length scales and solving a two-flavor scalar EWBG toy model exactly within a quantum Boltzmann equation formalism. It reveals a resonant enhancement of CP-violating charge generation when the flavor oscillation length $L_{ m osc}$ is comparable to the wall thickness $L_w$, and shows that diffusion of CP charge into the unbroken phase is significant. The authors demonstrate that the previous KPSS approach, which decoupled diagonal and off-diagonal density components, underestimates CP densities in the unbroken phase because its power counting breaks down in the resonant regime. The results underscore the necessity of treating the full density-matrix dynamics, including diffusion tails, and lay groundwork for incorporating fermions and realistic models to deliver robust, experimentally testable EWBG predictions.

Abstract

Electroweak baryogenesis (EWBG) in extensions of the Standard Model will be tested quantitatively in upcoming nuclear and particle physics experiments, but only to the extent that theoretical computations are robust. Currently there exist orders-of-magnitude discrepancies between treatments of charge transport dynamics during EWBG performed by different groups, each relying on different sets of approximations. In this work, we introduce a consistent power counting scheme (in ratios of length scales) for treating systematically the dynamics of EWBG: CP-asymmetric flavor oscillations, collisions, and diffusion. Within the context of a simplified model of EWBG, we derive the relevant Boltzmann equations using non-equilibrium field theory, and solve them exactly without ansatz for the functional form of the density matrices. We demonstrate the existence of a resonant enhancement in charge production when the flavor oscillation length is comparable to the wall thickness. We compare our results with the existing treatment of EWBG by Konstandin, Prokopec, Schmidt, and Seco (KPSS) who previously identified the importance of flavor oscillations in EWBG. We conclude: (i) the power counting of KPSS breaks down in the resonant regime, and (ii) this leads to substantial underestimation of the charge generated in the unbroken phase, and potentially of the final baryon asymmetry.

Figures (8)

• Figure 1: Precession of flavor polarization vectors about effective magnetic fields in the mass basis. In equilibrium, $\mathbf{p}= \bar{\mathbf{p}} = (0,0,n_B(\omega_1)-n_B(\omega_2))/2$ and the magnetic field $\mathbf{B}_0=(0,0,(\omega_1-\omega_2)/v_{\text{rel}})$ both point along the $\hat{\mathbf{z}}$ direction, and there is no precession. When the bubble wall turns on, it induces an additional magnetic field $\mathbf{B}_\Sigma$, causing $\mathbf{p},\mathbf{\bar{p}}$ to precess around $\mathbf{B}_0\pm \mathbf{B}_\Sigma$, which corresponds to flavor oscillations. If $\alpha' \neq 0$ so that there is CP-violation, $\mathbf{p},\mathbf{\bar{p}}$ develop different $\hat{\mathbf{z}}$ components, generating CP-asymmetric diagonal densities. In the adiabatic regime, $\mathbf{B}_\Sigma\ll \mathbf{B}_0$, the angle of precession is small, the system remains near equilibrium, and large CP asymmetries are not generated. In the non-adiabatic regime, $\mathbf{B}_\Sigma\gtrsim \mathbf{B}_0$, the precession angle is large, and large deviations from equilibrium and large CP asymmetries can arise. The precession is damped by collisions with $A$ bosons in the thermal bath, leading the system back to equilibrium at late time.
• Figure 2: Numerical results for particle and anti-particle density matrix for [top] a typical adiabatic bin: $k/T = 0.5, \cos\vartheta_k = 0.875$, and [bottom] a typical non-adiabatic bin, $k/T = 3.5, \cos\vartheta_k = 0.875$. Left panels display particle density matrix in Bloch decomposition: $p_{0} (k,\cos\vartheta_k,z)$ and $p_{x,y,z} (k,\cos\vartheta_k,z)$. Right panels display anti-particle density matrix: $\bar{p}_{0} (k,\cos\vartheta_k,z)$ and $\bar{p}_{x,y,z} (k,\cos\vartheta_k,z)$. Solid lines represent full numerical solutions, while dotted lines represent local thermal equilibrium results for diagonal components. See text for additional details.
• Figure 3: Diagonal CP asymmetries $k^2 (f_{11} (z) - \bar{f}_{11} (z))$ (in units of $\,T^2$), for three representative bins. The long-dashed line refers to a typical adiabatic bin $(k/T = 0.5, \cos\vartheta_k = 0.875)$, the short-dashed line to a mildly non-adiabatic bin $(k/T = 1.5, \cos\vartheta_k = 0.875)$, and the solid line to a typical non-adiabatic bin $(k/T = 3.5, \cos\vartheta_k = 0.875)$.
• Figure 4: Numerical results for the net charge densities $n_{1} (z)$ (solid line) and $n_{2}(z)$ (dashed line), in units of $\, T^3$, within the baseline model specified in Table \ref{['tab:baseline']}. In the unbroken phase ($z>L_{w}$) $n_{1}=n_L$ and $n_{2}=n_{R}$ (mass and flavor basis coincide). This plot illustrates the existence of diffusion tails in the unbroken phase. The relative size of the diffusion tails for $n_{1}$ and $n_{2}$ is as expected, given that $y_L > y_R$ in the baseline model.
• Figure 5: Resonant enhancement of $I_L^{CP}$, the total integrated $\Phi_L$ charge asymmetry in the unbroken phase [see Eq. \ref{['eq:ILR']}], as a function of the mass parameter $m_L$ (with fixed $m_R/T=2$) for different values of the wall thickness $L_{w}$: $L_{w} = 10/T$ (long-dashed curve), $L_{w} = 20/T$ (solid curve), $L_{w} = 40/T$ (short-dashed curve). All other input parameters are as in Table \ref{['tab:baseline']}.