Development of the electroweak phase transition and baryogenesis

TL;DR

This work analyzes the electroweak phase transition within a one-Higgs effective potential to quantify bubble nucleation and subsequent growth in a hot plasma, focusing on MSSM-like parameter choices. By computing the nucleation action $S_3$ and tracking bubble evolution, the authors establish upper and lower bounds on the transition temperature $T_t$ and show that the actual transition occurs in a narrow temperature slice near the nucleation onset. The study finds that bubble-wall thickness $l_w$, wall velocity $v_w$, and the Higgs order parameter $v(T_t)/T_t$ vary only modestly across the transition window, with MSSM-favored parameters yielding $l_w(T_t)\approx16/T$, $v_w(T_t)\sim3\times10^{-3}$, and $v(T_t)/T_t\gtrsim1.1$–$1.2$, supporting a viable, albeit delicate, window for electroweak baryogenesis. The results imply that estimations of $T_t$ based on $S_3(T)\!/T$ near nucleation are robust and that latent-heat reheating could influence baryogenesis in scenarios with strong damping, motivating further study of reheating effects.

Abstract

We investigate the evolution of the electroweak phase transition, using a one-Higgs effective potential that can be regarded as an approximation for the Minimal Supersymmetric Standard Model. The phase transition occurs in a small interval around a temperature T_t below the critical one. We calculate this temperature as a function of the parameters of the potential and of a damping coefficient related to the viscosity of the plasma. The parameters that are relevant for baryogenesis, such as the velocity and thickness of the walls of bubbles and the value of the Higgs field inside them, change significantly in the range of temperatures where the first-order phase transition can occur. However, we find that in the likely interval for T_t there is no significant variation of these parameters. Furthermore, the temperature T_t is in general not far below the temperature at which bubbles begin to nucleate.

Figures (7)

• Figure 1: Bubble radius and wall thickness of the nucleated bubbles vs the relative messure of the temperature, $\varepsilon$, for $D=1$, $E=0.06$, and $\lambda =2E$.
• Figure 2: Shape of the critical bubble at different temperatures.
• Figure 3: The minimum of the potential $v\left( T\right)$ and the value of $\phi$ inside the nucleated bubble, $\phi _{0}\left( T\right) \equiv \phi \left( r=0\right)$.
• Figure 4: Bubble wall velocity as a function of $\varepsilon$, for three different values of the damping coefficient $\eta$.
• Figure 5: Fraction of space in false vacuum as a function of $\varepsilon$, for $\eta =100$, $D=0.2$, $E=0.006$ and $\lambda =2E$.