Bubble Expansion and the Viability of Singlet-Driven Electroweak Baryogenesis

TL;DR

This work addresses how fast electroweak bubbles expand when a gauge singlet is dynamically involved during the phase transition. It extends previous wall-velocity computations to the real singlet extension of the SM (xSM) by combining kinetic theory with hydrodynamics, and considers both gauge-invariant and gauge-coupled potentials. The main findings show $v_w \gtrsim 0.2$ for moderately strong transitions, but very strong transitions can lack subsonic solutions, challenging non-local electroweak baryogenesis in some regions; gauge boson cubic terms further slow the walls in fast cases. The results have implications for baryogenesis viability and gravitational-wave spectra, and provide a framework to compute diffusion constants and characterize phase-transition dynamics in singlet-driven scenarios.

Abstract

The standard picture of electroweak baryogenesis requires slowly expanding bubbles. This can be difficult to achieve if the vacuum expectation value of a gauge singlet scalar field changes appreciably during the electroweak phase transition. It is important to determine the bubble wall velocity in this case, since the predicted baryon asymmetry can depend sensitively on its value. Here, this calculation is discussed and illustrated in the real singlet extension of the Standard Model. The friction on the bubble wall is computed using a kinetic theory approach and including hydrodynamic effects. Wall velocities are found to be rather large ($v_w \gtrsim 0.2$) but compatible with electroweak baryogenesis in some portions of the parameter space. If the phase transition is strong enough, however, a subsonic solution may not exist, precluding non-local electroweak baryogenesis altogether. The results presented here can be used in calculating the baryon asymmetry in various singlet-driven scenarios, as well as other features related to cosmological phase transitions in the early Universe, such as the resulting spectrum of gravitational radiation.

Figures (3)

• Figure 1: Illustration of the competing forces acting on the bubble wall that ultimately determine $v_w$. The steady state wall velocity is such that the vacuum energy difference between the phases ($\Delta V_{T=0}$) is balanced by the friction provided by the interactions of the wall with the plasma.
• Figure 2: Wall velocities for the xSM parameter space described in the text. The solid (dashed) curves depict the results neglecting (including) the $SU(2)_L$ gauge boson contributions to the finite temperature effective potential and friction. No subsonic solutions are found with $\phi_h(T_n)/T_n \gtrsim 1$ ($\gtrsim 1.1$) for the points in Set 1 neglecting (including) the gauge bosons. The curves corresponding to Set 2 would extend beyond $\phi_h(T_n)/T_n=1.1$, however the perturbative fluid approximation begins to break down significantly for stronger transitions, and so we restrict our results to the region shown. The red dotted line shows the speed of sound in the plasma, above which non-local electroweak baryogenesis is not possible. Note that we have searched exclusively for subsonic solutions to the equations of motion.
• Figure 3: Late-time bubble wall profiles relevant for electroweak baryogenesis obtained by solving the wall equations of motion. The solid (dashed) curves depict the results neglecting (including) the $SU(2)_L$ gauge boson contributions to the finite temperature effective potential and friction. The top panel shows the singlet field offset, while the bottom two show the SM-like Higgs and singlet wall widths. Bubbles with strong first-order phase transitions tend to feature $L_{h,s}\sim 5/T$ and the singlet lagging slightly behind the Higgs field.