Exploring dynamical $CP$ violation induced baryogenesis by gravitational waves and colliders

By assuming a dynamical source of $CP$ violation, the tension between sufficient $CP$ violation for successful electroweak baryogenesis and strong constraints from current electric dipole moment measurements could be alleviated. We study how to explore such scenarios through gravitational wave detection, collider experiments, and their possible synergies with a well-studied example.

Figure 1

Parameter spaces for a large washout parameter for $\kappa =1.0$ and $\kappa =2.0$, respectively.

Figure 2

Left: Main branching ratios and total decay width of $S$ with different $m_S$. In this plot, we set $a$, $b$, and $\mathrm{\Lambda }$ as 1, 1, and 1 TeV, respectively. The mass gap around 125 GeV comes from the $S-H$ mixing term $\mathrm{\Delta }{m}_{HS}^2=a\frac{3m_t^4}{2{\pi }^2\mathrm{\Lambda }v}$. The $S-H$ mixing term changes the $S$ property hugely when $m_S$ is close to $m_H$. Right: $S-H$ field mixing versus $m_S$ plot. Maximal mixing is obtained when $m_S$ is approaching the boundary of the mass gap.

Figure 3

Current exclusion limit and future search sensitivity projected on $\mathrm{\Lambda }$ versus $m_S$ plane. In both plots, regions between black dashed lines are forbidden by mass mixing term $\mathrm{\Delta }{m}_{HS}^2=a\frac{3m_t^4}{2{\pi }^2\mathrm{\Lambda }v}$; regions below dotted blue lines have been excluded by EDM measurement; regions below dashed red lines have been excluded by collider scalar searches and Higgs data. In the left plot, regions below dash dotted olive lines can be observed from $ZS$ production at $5{\mathrm{ab}}^{-1}$ CEPC with a C.L. higher than $5\sigma$. In the right plot, we show the ratio $\frac{\sigma (HZ)}{{\sigma }_{\mathrm{SM}}(HZ)}$ with purple dash dotted contour lines. In the plot, we set $a=b=1$ and $\kappa =2$.

Figure 4

Representative Feynman diagrams that contribute to the $gg\to SH$ process.

Figure 5

Leading-order differential cross section for the $gg\to SH$ process, with $\kappa =2$, $m_S=115\mathrm{GeV}$, $\mathrm{\Lambda }=1\mathrm{TeV}$, and $\sqrt{s}=14\mathrm{TeV}$. The separate contributions from the diagrams are shown in different color schemes. ”tris” (magenta) represents the cross section considering only the first type of diagrams as in Fig. 4, “tri4” (red) represents the second, and “box” (green) represents the last. The blue curve shows the cross section including the tri4 and the box contributions. The black curve is the total cross section including all diagrams and their interference, which is dominated by the tris or $\kappa$ term at a low energy scale and by the dimension-five $\eta$ term and interference at a high energy scale.

Figure 6

Left: $\mu \mu$ recoil mass distribution for the SM background and signal, with $\mathrm{\Lambda }=1\mathrm{TeV}$ and $m_S=115\mathrm{GeV}$. Right: $\mu \mu$ recoil mass distribution for the SM background and signal, with $\mathrm{\Lambda }=1\mathrm{TeV}$ and $m_S=135\mathrm{GeV}$. Vertical dotted black lines represent the mass window we choose. Luminosity is taken at $5{\mathrm{ab}}^{-1}$ following the CEPC report. The $y$ axis represents the number of events per bin, which is taken to be 0.25 GeV.

Figure 7

The correlation between the GW spectrum and the associated collider signals for the benchmark sets with $\kappa =2$ and $\mathrm{\Lambda }=1\mathrm{TeV}$. The colored regions depict the expected sensitivities from the future GW experiments LISA, BBO, and U-DECIGO, respectively. The black line represents the phase transition GW spectrum for the benchmark sets at $m_S=115\mathrm{GeV}$, which is related to the detectable lepton collider signal with a cross section $\sigma (SZ)=13.6\mathrm{fb}$ at CEPC. The green line represents the case for another benchmark set at $m_S=135\mathrm{GeV}$.