Electroweak phase transition in the scale invariant standard model

In an extension to the scale invariant standard model by two real singlet scalars $s$ and $s^{\prime }$ in addition to the Higgs field, we investigate the strong first-order electroweak phase transition as a requirement for baryogenesis. This is the minimal extension to the scale invariant standard model with two extra degrees of freedom that possesses the physical Higgs mass of 125 GeV. The scalar $s^{\prime }$ being stable because of the ${\mathbb{Z}}_2$ discrete symmetry is taken as the dark matter candidate. We then show that the electroweak phase transition is strongly first order, the dark matter relic density takes the desired value ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2\sim 0.11$, and the constraints from direct detection experiments are respected only if $m_{s^{\prime }}\equiv m_{\mathrm{DM}}\gtrsim 4.5\mathrm{TeV}$. The model also puts a lower bound on the scalon mass, $m_s\gtrsim 200\mathrm{GeV}$.

Figure 1

The plot compares the dark matter mass against the coupling ${\lambda }_{hs}$ with the washout criterion satisfied and ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2\sim 0.11$.

Figure 2

A histogram for the ratio $v_c/T_c$ with the correct relic density $\mathrm{\Omega }{h}^2\sim 0.11$. It is shown that $v_c/T_c\gtrsim 4$, which guarantees a very strong first-order phase transition.

Figure 3

The viable range of the DM mass is $m_{\mathrm{DM}}\gtrsim 4.5\mathrm{TeV}$ after imposing the XENON1t/LUX direct detection experiments on the DM-nucleus elastic scattering cross section, the DM relic density constraint, and the first-order phase transition condition.

Figure 4

The plot shows the viable range of the scalon mass being $m_s\gtrsim 200\mathrm{GeV}$.