Benchmarking a fading window: electroweak baryogenesis in the C2HDM, LHC constraints after Run 2 and prospects for LISA

TL;DR

The paper evaluates electroweak baryogenesis in the CP-violating complex 2HDM (C2HDM) by confronting EWPT-strong regions with LHC Run 2 (13 TeV) constraints and forecasting gravitational wave signals for LISA. It defines four CP-sensitive benchmark planes (BP-SG, BP-ISG, BP-ASG, BP-AMD) to map the interplay between a strong first-order EWPT, BAU viability, EDM tension, and GW observability, using tools like HiggsTools, BSMPT, and Barr–Zee EDM computations. The study finds that CP violation tends to weaken the EWPT, and current electron EDM bounds tightly constrain the BAU-favorable regions, with only limited overlap where both EWBG and detectable GW signals coexist (notably in BP-SG and BP-ASG). Across all benchmarks, LHC multi-Higgs signatures remain the most powerful probes of the viable space, while GW signals in LISA are only potentially detectable in a narrow subset; the results highlight a sharp tension between EWBG in the C2HDM and EDM constraints, suggesting the need for extended models or CP-violating mechanisms beyond the minimal setup.

Abstract

The origin of the baryon asymmetry of the universe remains one of the most pressing open questions in particle physics and cosmology. Electroweak baryogenesis offers an experimentally testable explanation, requiring new sources of CP violation and a strong first-order electroweak phase transition.The Two Higgs doublet model (2HDM) is the simplest scalar extension of the Standard Model that can accommodate both ingredients. We critically assess the viability of the complex 2HDM (C2HDM) (a 2HDM with a softly broken $\mathbb{Z}_2$ symmetry and a single source of explicit CP violation in the Higgs sector) as a framework for electroweak baryogenesis, incorporating for the first time a comprehensive set of LHC Run 2 results at 13 TeV. By defining CP-violating benchmark planes tailored for a strong first-order electroweak phase transition, we identify regions of parameter space motivated by electroweak baryogenesis that will be testable at the LHC, and at future space-based gravitational wave experiments. The benchmark planes are intended to guide ongoing efforts in defining representative scenarios for the exploration of CP-violation in extended scalar sectors at the LHC Run 3 and beyond, while also assessing the emerging synergy between the LHC and future gravitational wave observatories such as LISA. We also quantify the current tension between the realisation of electroweak baryogenesis and the non-observation of the electron electric dipole moment (EDM), finding that the predicted electron EDMs typically exceed the experimental limits by at least an order of magnitude.

Figures (3)

• Figure 1: Shown are parameter points in the $\{\sin(\beta - \alpha_1), \alpha_3\}$ planes that predict a strong first-order EWPT, with the color of each point indicating the corresponding value of $\xi_n$. The remaining C2HDM parameters are fixed as specified in the plot headers. The grey shaded areas are excluded by cross section limits from BSM scalar searches at the LHC. The green area indicates parameter space regions featuring a GW signal with a LISA SNR larger than SNR $>10^{-3}$ assuming an exposure time of 7 years. Taking into account the sizable theoretical uncertainties, these areas can potentially be probed with LISA (see the text for details). The blue area indicates parameter regions with the baryon-to-entropy ratio $\eta_s$ predicted to be in the range $\eta^{\rm exp}_s / 2 \leq \eta_s \leq 2\eta^{\rm exp}_s$. Finally, the dashed black lines are contour lines indicating the prediction for the electron EDM $|d_e|$. In the lower plot no green and blue regions are visible because the EWPT is not sufficiently strong to give rise to a detectable GW signal or to a baryon-to-entropy ratio in agreement with observations, respectively.
• Figure 2: Shown are parameter points with a strong first-order EWPT in a $\{ t_\beta ,\alpha_3\}$ plane in the upper plot and a $\{ s_{\beta - \alpha_1}, \alpha_3\}$ plane in the lower plot. The colour coding of the points and the grey, blue and green regions are defined as in \ref{['fig:cpsmoker1']}. In the lower plot no green region is visible because the EWPT is not sufficiently strong to give rise to a detectable GW signal.
• Figure 3: Predictions for $L_w T_n$ against $\alpha$ for the benchmark planes defined in \ref{['sec:results']}. BP-ASG: aligned smoking gun scenario (blue), BP-SG: smoking gun scenario (orange), BP-ISG: inverted smoking gun scenario (green), BP-AMD: almost mass degenerate scenario (red). The horizontal dotted line indicates the value $L_w T_n = 2$, where the gradient expansion of the bubble wall profile becomes unreliable.