Perturbative analysis of the electron electric dipole moment and $CP$ violation in two-Higgs-doublet models

I consider a general two-Higgs-doublet model with $CP$ violation. I give a perturbative expansion for the mass eigenstates in terms of the small $CP$-violating phase. I use these analytical expressions to show that $\mathcal{O}({10}^{-2})$ $CP$ violation is allowed by the experimental bounds on the electron electric dipole moment in some regions of the parameter space. These regions also include parameters that are expected to give a strongly first-order electroweak phase transition required for electroweak baryogenesis. I also comment on how to incorporate the $CP$ violation into the searches for a strongly first-order electroweak phase transition which could explain the matter/antimatter asymmetry in the Universe.

Figure 1

Probability of $CP$-odd decays of ${\tilde{h}}^0$ [$b=\frac{({\lambda }_6-{\lambda }_5)c_{\beta }}{{\lambda }_6-2{\lambda }_h}$] vs ${\lambda }_6$ for $\tan \beta =1$, $\alpha -\beta =\frac{\pi }{2}$, $\alpha -\beta =\frac{\pi }{2}$, $m_{\tilde{H}}=500\mathrm{GeV}$, $\text{Re}({\mu }_3^2)=5\times {10}^4{\mathrm{GeV}}^2$, and $\xi =0.01$.

Figure 2

Top-loop diagram contributing to the electron EDM. Boson-loop diagrams are similarly two-loop diagrams but include $W/Z$ bosons in the loops (for example, exchanging the top loop for a $W$ loop).

Figure 3

Electron EDM vs $\xi$ plot for ${\lambda }_6=5$ ($m_{\tilde{A}}\simeq 375–405\mathrm{GeV}$), $m_{\tilde{H}}=500\mathrm{GeV}$, $\tan \beta =1$, $\alpha -\beta =\frac{\pi }{2}$. The gray region is experimentally excluded.

Figure 4

Electron EDM vs $\xi$ plot for ${\lambda }_6=15$ ($m_{\tilde{A}}\simeq 670–690\mathrm{GeV}$), $m_{\tilde{H}}=500\mathrm{GeV}$, $\tan \beta =1$, $\alpha -\beta =\frac{\pi }{2}$. The gray region is experimentally excluded.

Figure 5

Electron EDM vs $\xi$ plots for $\tan \beta =1–3$ and for (a) ${\lambda }_6=5$, $\text{Re}({\mu }_3^2)={10}^4{\mathrm{GeV}}^2$ and (b) ${\lambda }_6=15$, $\text{Re}({\mu }_3^2)=5\times {10}^4{\mathrm{GeV}}^2$. The following parameters are used in both plots: $m_{\tilde{H}}=500\mathrm{GeV}$, $\alpha -\beta =\frac{\pi }{2}$.