Bubbles in the supersymmetric standard model

TL;DR

The paper tackles electroweak baryogenesis in the MSSM by computing the tunneling probability from the symmetric to the broken phase and the accompanying Higgs bubble profiles using a resummed two-loop finite-temperature potential, with a focus on the light-stop region. The authors develop a two-Higgs MSSM framework, solve for the bubble bounce, and quantify the wall thickness $L_\omega$ and the change in Higgs mixing along the wall via $\Delta\beta$, showing that two-loop corrections markedly strengthen the phase transition and the generated baryon asymmetry. At a representative parameter point, they find $T_c \approx 95.2$ GeV and $S_3(T_c)/T_c \approx 140$–$145$, while two-loop effects boost $\Delta\beta$ and the baryogenesis integral $I$ by more than an order of magnitude relative to one-loop results. They further show that squark-induced negative modes do not destabilize the bounce in the allowed region, reinforcing the robustness of the mechanism. Overall, the work provides quantitative, two-loop-backed predictions for bubble properties that enhance MSSM electroweak baryogenesis viability in the light-stop scenario and informs collider-era tests of the model.

Abstract

We compute the tunneling probability from the symmetric phase to the true vacuum, in the first order electroweak phase transition of the MSSM, and the corresponding Higgs profiles along the bubble wall. We use the resummed two-loop temperature-dependent effective potential, and pay particular attention to the light stop scenario, where the phase transition can be sufficiently strongly first order not to wipe off any previously generated baryon asymmetry. We compute the bubble parameters which are relevant for the baryogenesis mechanism: the wall thickness and $Δβ$. The two-loop corrections provide important enhancement effects, with respect to the one-loop results, in the amount of baryon asymmetry.

Figures (6)

• Figure 1: The Euclidean action as a function of the temperature for $m_Q=1$ TeV, $\tan\beta=2.5$, $\widetilde{A}_t=0$, $m_{\;\widetilde{t}}=150$ GeV, and $m_A=200$ GeV.
• Figure 2: The Higgs profile $\rho(r)/v(T)$ for $T=T_c+0.4$ GeV (long-dashed curve) and $T=T_c-0.4$ GeV (short-dashed curve), and values of supersymmetric parameters as in Fig. 1.
• Figure 3: The same as in Fig. 2 but for the Higgs profile $\Delta\beta(r)$.
• Figure 4: Higgs profile $\rho(r)/v(T_c)$ for $m_Q=1$ TeV, $\tan\beta=2.5$, $\widetilde{A}_t=0$, $m_{\;\widetilde{t}}=150$ GeV, and $m_A=100$ GeV (thick-solid curve), 200 GeV (long-dashed curve), 300 GeV (short-dashed curve) and 400 GeV (thin-solid curve).
• Figure 5: The parameter $\Delta\beta$ in the two-loop (solid curve) and one-loop (dashed curve) approximations, for $m_Q=1$ TeV, $\tan\beta=2.5$, $\widetilde{A}_t=0$ and $m_{\;\widetilde{t}}=150$ GeV, as a function of $m_A$.