Towards a scale free electroweak baryogenesis

We propose a new electroweak baryogenesis scenario in high-scale supersymmetric (SUSY) models. We consider a singlet extension of the minimal SUSY standard model introducing additional vectorlike multiplets. We show that the strongly first-order phase transition can occur at a high temperature comparable to the soft SUSY breaking scale. In addition, the proper amount of the baryon asymmetry of the Universe can be generated via the lepton number violating process in the vectorlike multiplet sector. The typical scale of our scenario, the soft SUSY breaking scale, can be any value. Thus our new electroweak baryogenesis scenario can be realized at arbitrary scales, and we call this scenario scale free electroweak baryogenesis. This soft SUSY breaking scale is determined by other requirements. If the soft SUSY breaking scale is $\mathcal{O}(10)\mathrm{TeV}$, our scenario is compatible with the observed mass of the Higgs boson and the constraints by electric dipole moment measurements and flavor experiments. Furthermore, the singlino can be a good candidate for dark matter.

Figure 1

The outline of the thermal history of our scenario. (a) At high enough temperatures compared to $\mathcal{O}(M_{\mathrm{SUSY}})$, the potential for the Higgs field is lifted. (b) The first-order phase transition of the Higgs field and EWBG occur at $T=T_{1\mathrm{st}}$. (c) After EWBG, the Higgs field is trapped at the breaking vacuum, $T_{1\mathrm{st}}>T>T_{\mathrm{r}\mathrm{o}\mathrm{l}\mathrm{l}}$. (d) The Higgs field returns to the symmetric vacuum again, $T_{\mathrm{r}\mathrm{o}\mathrm{l}\mathrm{l}}>T$. (e) After the temperature becomes lower than the electroweak scale, the Higgs field settles down at the electroweak symmetry breaking vacuum. More details are given in the text.

Figure 2

The potential for the Higgs field $V_{\min }(\varphi ,T)$ as a function of $\varphi$ with varying temperatures $T$. ${\varphi }_s$ and $\tan \beta$ are calculated to minimize the potential for each given $\varphi$ and $T$. Here, we subtract the constant term from the potential to set $V_{\min }(\varphi =0,T)=0$. The region with small $\varphi$ is enlarged in the right figure.

Figure 3

The blue lines correspond to the classical action $S(T)$ for the three-dimensional (${\varphi }_1,{\varphi }_2,{\varphi }_s$) bounce solution. The red lines correspond to $\mathrm{\Delta }\varphi /T$. We take ${\lambda }_1^2=0.49$ (dashed lines), 0.50 (thick lines), and 0.55 (dotted lines). The gray line represents $S(T)=130$ and $\mathrm{\Delta }\varphi /T=0.9$.

Figure 4

The bounce solution profile for the first-order phase transition at the benchmark point. The horizontal axis is the space coordinate $r$ normalized by $m_{s,0}$. $r=0$ corresponds to the center of the bubble. The blue lines indicate the field values of ${\varphi }_1$, ${\varphi }_2$, and $-{\varphi }_s$. The red line corresponds to $\tan \beta$.

Figure 5

The scatter plot in the $\tan {\beta }_{\text{vac}}-M_{\text{charged}}$ plane. The red shaded region shows the region excluded by the $\overline{B}\to X_s\gamma$ search. At all points the first-order phase transition [${}^{\exists }S(T)<130$] occurs. At the green points the strongly first-order phase transition [$\mathrm{\Delta }\varphi /T>0.9$] occurs. The star corresponds to the benchmark point.