Reassessing CP Violation in the C2HDM with Machine Learning

TL;DR

The paper tackles CP violation in the complex 2-Higgs Doublet Model (C2HDM) under stringent eEDM and collider constraints. It deploys ML-assisted parameter-space exploration using an Evolutionary Strategy with Novelty Reward to uncover viable regions, explicitly incorporating the complete two-loop eEDM calculation with kite diagrams and charm Barr-Zee diagrams. The study shows that kite diagrams are essential for gauge-invariant eEDM results and that charm contributions must be included at current experimental precision; with careful cancellations, sizable CP-odd Higgs-fermion couplings remain viable in Type-II and Flipped setups when $h_{125}$ coincides with $h_2$, and even under anticipated tighter EDM limits down to $10^{-33}$ e cm. The findings emphasize the need for direct CP probes at the LHC and motivate refined EDM measurements, while revealing subtle scheme- and mass-dependence features and highlighting the potential for CP-violating signals away from exact alignment in certain model realizations.

Abstract

We provide a study of the parameter space of the complex 2-Higgs Doublet Model (C2HDM), focusing on signs of large CP-violating couplings of the 125 GeV Higgs boson with the fermions. The study is performed utilizing Machine Learning (ML) techniques developed recently for parameter space exploration, including an Evolutionary Strategy Algorithm and Novelty Reward. We give particular attention to the electron electric dipole moment (eEDM). We confirm that the recently found kite diagrams are crucial for the outcome of the analysis. Moreover, their use also mitigates the dependence of the results on the scale and scheme choice of the masses in the loop diagrams. We furthermore point out that, already at the current level of experimental precision, the Barr-Zee diagrams with charm quark loops must be taken into account. The combined use of kite diagrams and ML techniques allows for the resurrection of large fermion CP-odd couplings for Type-II and Flipped C2HDM when the 125 GeV Higgs coincides with the second lightest neutral scalar. This arises due to cancellations, typically of the per-mil order, which, moreover, will still be possible for a foreseeable eEDM precision down to $10^{-33}$ e.cm. For these cases, the constraints on the CP-odd couplings arises from the precision LHC measurements.

Figures (13)

• Figure 1: Points on the plane $\text{sign}(k_V)c_b^o \,\, \text{vs.} \,\, \text{sign}(k_V)c_b^e$ obtained with Strategy 1 in the Type-II C2HDM with $h_{125}=h_2$. The purple points include all constraints, including those relative to $\theta_\tau$ implemented via HS, while the red points include all constraints except those relative to $\theta_\tau$. Left panel: current eEDM limit $4.1\times 10^{-30} \,\mathrm{e\cdot cm}$. Right panel: projected eEDM limit $1.0\times 10^{-33} \,\mathrm{e\cdot cm}$. See text for details.
• Figure 2: Different contributions to the eEDM for the set of points sampled: total contribution (blue), total contribution except for the kite diagrams (red), contribution of the dominant class of diagrams (green). Left panel: current eEDM limit $4.1\times 10^{-30} \,\mathrm{e\cdot cm}$. Right panel: projected eEDM limit $1.0\times 10^{-33} \,\mathrm{e\cdot cm}$ .
• Figure 3: Points on the plane $\text{sign}(k_V)c_b^o \,\, \text{vs.} \,\, \text{sign}(k_V)c_b^e$ obtained with Strategy 2 in the Type-II C2HDM with $h_{125}=h_2$. Red points pass all constraints except those on $\theta_\tau$; the remaining points additionally impose the latter constraint: either via HS (in purple) or via Eq. (\ref{['theta_tau']}) (in blue). Left: eEDM calculated in the $M_Z$-masses scheme. Right: eEDM calculated in the pole-masses scheme.
• Figure 4: Points obtained with Strategy 2 in the Type-II C2HDM with $h_{125}=h_2$, on the plane eEDM prediction (calculated with the pole-masses scheme) vs. $\text{sign}(k_V) c_b^o$. The color code shows the lowest possible $\chi^2$ calculated with HS.
• Figure 5: The same as the left panel of Fig. \ref{['fig:MLpoints_17_tau']}, but considering exclusively points with $m_{1} \leq 60\textrm{GeV}$.