Bubble Walls, CP Violation and Electroweak Baryogenesis in the MSSM

TL;DR

The paper investigates electroweak baryogenesis in the MSSM by modeling a strong first‑order phase transition with a two‑Higgs wall, using a semi‑classical WKB transport framework to connect CP‑violating wall physics to the baryon asymmetry via sphalerons. It develops robust numerical methods to compute stationary bubble walls in multi‑scalar theories, analyzes CP violation (both explicit and transitional) in the wall, and derives diffusion equations to quantify the resulting baryon asymmetry. The results indicate that MSSM CP violation must be large or finely tuned to generate the observed asymmetry, with transitional CP violation unlikely in the MSSM parameter space, while NMSSM scenarios offer more natural CP‑violating wall dynamics. The work provides a quantitative framework linking wall profiles, CP phases, wall velocity, diffusion, and sphaleron processes, with implications for EDM constraints and extensions beyond the MSSM.

Abstract

We discuss the generation of the baryon asymmetry by a strong first order electroweak phase transition in the early universe, particularly in the context of the MSSM. This requires a thorough numerical treatment of the bubble wall profile in the case of two Higgs fields. CP violating complex particle masses varying with the Higgs field in the wall are essential. Since in the MSSM there is no indication of spontaneous CP violation around the critical temperature (contrary to the NMSSM) we have to rely on standard explicit CP violation. Using the WKB approximation for particles in the plasma we are led to Boltzmann transport equations for the difference of left-handed particles and their CP conjugates. This asymmetry is finally transformed into a baryon asymmetry by out of equilibrium sphaleron transitions in the symmetric phase. We solve the transport equations and find a baryon asymmetry depending mostly on the CP violating phases and the wall velocity.

Figures (9)

• Figure 1: Pseudo-Langevin method: Large time steps allow to overcome small bumps and troughs. Small time steps or simple minimum finding routines may lead into undesired local minima.
• Figure 2: Solution and ansätze in the NMSSM. Left top: Fitted $\tanh(x/L+{\hat{x}})$-ansatz and the ridge lying directly near the actual solution. Lower left: Shape of solution versus $x$ compared to a kink ansatz. Right: 3-dimensional views of the effective potential with solution and kink ansatz.
• Figure 3: Dominant 1-loop effect: $m_3$ in dependence of $A_t$ and $\mu$ including stops and charginos. The tree level contribution causes a shift in the mean $m_3^2$. Large values with equal signs are preferred to give a negative contribution to $m_3^2$.
• Figure 4: Relative number versus value of $m_3^2$. Small positive values are preferred.
• Figure 5: Correlation of $m_3^2$ and the Higgs mass $m_H$. Most favorable values are correlated with unphysical small Higgs values.