Velocity of electroweak bubble walls

TL;DR

The paper investigates bubble-wall velocities during the electroweak phase transition across several Standard Model extensions, focusing on friction from thermal particles and infrared bosons and the impact of hydrodynamics. Using a thin-wall, bag EOS framework and a tractable friction model, it computes wall velocities for detonations and deflagrations and maps how $T_n$, latent heat $L$, and the friction parameter $\eta$ set $v_w$. The study finds that deflagrations are generally more common, but strongly first-order transitions driven by extra bosons can yield high wall velocities ($v_w$ up to ~0.6), while models with strongly coupled extra fermions tend to produce smaller velocities ($v_w\sim 10^{-2}-10^{-1}$), relevant for baryogenesis. Overall, the results show that wall dynamics—and thus gravitational wave production and baryogenesis prospects—depend sensitively on the particle content and couplings to the Higgs, with fermion-rich models favoring BAU and boson-rich models favoring GW signals, though both can be significant depending on parameter choices.

Abstract

We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, $0.1\lesssim v_w\lesssim 0.6$. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermions which are strongly coupled to the Higgs boson may provide a strongly first-order phase transition and small velocities, $10^{-2}\lesssim v_w\lesssim 10^{-1}$, as required by electroweak baryogenesis.

Figures (10)

• Figure 1: The contribution of a complex singlet to the friction as a function of the coupling $h$ for $\mu =0$ and $m_{H}=125GeV$.
• Figure 2: The contribution of a complex singlet to the friction as a function of $\mu$ for $h=1$ and $m_{H}=125GeV$.
• Figure 3: The friction coefficient for the SM with a complex singlet as a function of the coupling $h$ for $m_{H}=125GeV$ and $\mu =0$ is plotted in solid line. The dashed line corresponds to using the small $m/T$ approximations.
• Figure 4: The wall velocity as a function of the coupling $h$ of the singlet, for several Higgs masses. All the curves correspond to the case $\mu =0$, except for the doted line, which corresponds to $\mu=100GeV$. The crosses indicate the case $\phi_n/T_n=1$.
• Figure 5: The wall velocity as a function of $\mu$, for $m_{H}=125GeV$ and three values of $h$.