The bubble wall velocity in the minimal supersymmetric light stop scenario

TL;DR

The paper computes the bubble wall velocity during a strong first-order electroweak phase transition in the minimal supersymmetric light stop scenario using a 2-loop finite-temperature potential. It models friction with a single parameter calibrated to 1-loop MSSM results and solves relativistic hydrodynamics coupled to the Higgs field, finding a subsonic v_w ~ 0.05 that remains robust for Higgs masses near 115 GeV. The 2-loop corrections strengthen the phase transition by about 10% when evaluating the true bubble interior, and friction is significantly enhanced relative to SM-like cases, influencing baryogenesis and gravitational-wave expectations. The study highlights the importance of precise interior bubble conditions (v_b/T_b) for washout criteria and sets the stage for exploring related scenarios beyond the MSSM.

Abstract

We build on existing calculations of the wall velocity of the expanding bubbles of the broken symmetry phase in a first-order electroweak phase transition within the light stop scenario (LSS) of the MSSM. We carry out the analysis using the 2-loop thermal potential for values of the Higgs mass consistent with present experimental bounds. Our approach relies on describing the interaction between the bubble and the hot plasma by a single friction parameter, which we fix by matching to an existing 1-loop computation and extrapolate it to our regime of interest. For a sufficiently strong phase transition (in which washout of the newly-created baryon asymmetry is prevented) we obtain values of the wall velocity, v_w~0.05, far below the speed of sound in the medium, and not very much deviating from the previous 1-loop calculation. We also find that the phase transition is about 10% stronger than suggested by simply evaluating the thermal potential at the critical temperature.

Figures (3)

• Figure 1: Values of the strength of the phase transition $\xi = \frac{v_c}{T_c}$ and the Higgs mass in the region of parameter space (with $\tan \beta = 4$) of interest for baryogenesis. For this value of $\tan \beta$ the right-handed stop mass (we assume no mixing) varies in this range from $m_{\tilde{t}_R} \sim 135.2$ to $m_{\tilde{t}_R} \sim 138.8$ GeV and the left-handed-stop mass is given by $m_Q$ in units if GeV.
• Figure 2: Linear extrapolation of $\eta$ values to the $m_U^2$ region of interest for $\tan\beta=4$ (solid line, calibration values from John:2000zq as triangles), $\tan \beta = 6$ (dashed line, calibration values as crosses). $m_{\tilde{t}_R} \in [135.2, 184.1]$ GeV (almost no dependence on $\tan\beta$)
• Figure 3: Values of $\xi = v/T$ for the case $\tan \beta = 4$, $m_Q = 14,000$ GeV ($m_h \sim 112$ GeV) at the critical and nucleation temperatures and in the broken symmetry phase where sphalerons must be suppressed to avoid washing out the newly-generated baryon asymmetry.