The Electric Dipole Moment of the electron in the decoupling limit of the aligned Two-Higgs Doublet Model

TL;DR

This work analyzes the electron EDM in the decoupling limit of the aligned two-Higgs doublet model (A2HDM), identifying Barr-Zee-type two-loop contributions that arise from a heavy scalar sector with new CP-violating phases. The authors show that these logarithmically enhanced effects can be described model-independently within the SMEFT as mixing among dimension-6 operators, notably through $Q_{eH}$, $Q_{ledq}$, and $Q_{lequ}^{(1,3)}$ feeding the dipole operator $\mathscr{C}_{e\gamma}$; the resulting double and single logarithms scale as $\log^2(M^2/m_t^2)/M^2$ and $\log(M^2/m_t^2)/M^2$, respectively, and are absent in $\\ Z_2$-symmetric 2HDMs. Using a detailed benchmark and phenomenological scans, the paper demonstrates that charged-current fermion-loop Barr-Zee diagrams can dominate the eEDM and that complex alignment phases can allow relatively light new scalars while respecting experimental bounds, due to cancellations among contributions. The results highlight a clear link between high-scale CP-violating scalar sectors and low-energy EDM observables through SMEFT RG running and operator mixing, offering a framework for global fits and future explorations of CP violation beyond the Standard Model.

Abstract

We present a discussion of model-independent contributions to the EDM of the electron. We focus on those contributions that emerge from a heavy scalar sector that is linearly realized. In particular, we explore the decoupling limit of the aligned 2HDM. In this model, Barr-Zee diagrams with a fermion loop produce logarithmically-enhanced contributions that are proportional to potentially large new sources of CP violation. In the decoupling limit these contributions are generated by effective dimension-6 operators via the mixing of four-fermion operators into electroweak dipole operators. These logarithmic contributions are not present in more constrained versions of the 2HDM where a $\mathcal Z_2$ symmetry is imposed, which then controls the basis of effective operators needed to describe the new physics contributions to the electron EDM. Thus, the $\mathcal Z_2$ symmetry provides a suppression mechanism. In the course of the comparison of the results from the aligned 2HDM with the leading logarithms from SMEFT, we needed to specify or correct signs of expressions found in the literature. We then study how the experimental bounds on the electron EDM constrain the set of parameters of the aligned 2HDM.

Figures (11)

• Figure 1: One-loop diagram for the eEDM in the A2HDM.
• Figure 2: Charged-current Barr-Zee diagrams with a fermion loop. Here, $q_u$ and $q_d$ are up-type and down-type quarks.
• Figure 3: Scatter plot of the eEDM in the A2HDM as a function of $M$, at the benchmark point Eq. \ref{['eq:benchmark_values']}. The absolute values of the alignment parameters are taken as: $|\varsigma_u|=0.03$, $|\varsigma_d|=0.3$ and $|\varsigma_l|=0.6$. The blue dots correspond to the full A2HDM, while the expression at the origin of the orange dots does not include charged-current (CC) fermion-loop Barr-Zee contributions. The black line assumes real alignment parameters $\varsigma_i$. The gray bands show the upper bound on the modulus of the eEDM from Eq. \ref{['eq:current_exp_value']}.
• Figure 4: Approximations to predictions of the eEDM in the A2HDM as a function of $M$, at the benchmark point in Eq. \ref{['eq:benchmark_values']}. The black line is the full two-loop result in the A2HDM. The solid red curve is the leading squared logarithmic approximation, and the dashed blue curve includes some sub-leading logarithms from SMEFT. The shaded blue region is obtained by varying the UV scale from $M/2$ up to $2M$. The $\mathcal{Z}_2$-symmetric case carries no large squared-logarithm in the decoupling limit.
• Figure 5: EM and NC Barr-Zee diagrams with a fermion loop.