Z and Higgs Factory Implications of Two Higgs Doublets with First-Order Phase Transitions

TL;DR

This work investigates CP-conserving 2HDMs as hosts for a strong first-order electroweak phase transition (SFOEWPT) and their testability at future $e^+e^-$ colliders (FCC-ee/CEPC). By computing the finite-temperature effective potential $V_{eff}(T)$ with $V_{eff}(T)=V_{tree}(0)+V_{CW}(0)+V_{CT}(0)+V_T(T)+V_{daisy}(T)$ and scanning a wide 2HDM parameter space using $BSMPTv3$, the authors identify regions with $\xi_p=v_p(T_p)/T_p>1$ that realize SFOEWPT while satisfying theoretical and experimental constraints. They then study how projected electroweak precision observables (EWPO, notably the oblique parameters $S$ and $T$) and HL-LHC searches for exotic Higgs states restrict these regions, finding that EWPO strongly favor the alignment limit and the $hZ$ cross section at an $e^+e^-$ collider can reveal non-decoupled radiative corrections even when $Z$-pole data are SM-like. At $\sqrt{s}\approx 240$ GeV, NLO corrections to $e^+e^-\to hZ$ can exceed the experimental sensitivity $\Delta\sigma/\sigma\sim 0.31\%$, enabling discovery prospects for BSM Higgs-sector effects tied to SFOEWPT. Overall, precision lepton colliders offer a powerful, largely model-independent probe of BSM Higgs dynamics and the cosmological history of electroweak symmetry breaking, complementary to HL-LHC searches.

Abstract

We investigate the potential of future electron-positron colliders, such as FCC-ee and CEPC, to probe 2-Higgs-doublet models (2HDMs) that facilitate a strong first-order electroweak phase transition (SFOEWPT), a necessary condition for electroweak baryogenesis. Focusing on a 2HDM in the CP-conserving limit, we identify parameter regions consistent with an SFOEWPT and evaluate their compatibility with projected precision electroweak and Higgs measurements, as well as searches for exotic Higgs bosons. We show that radiative corrections to $e^+e^-\to hZ$ production introduce deviations in the cross section that are resolvable with the anticipated sub-percent precision at lepton colliders even when experimental outcomes of the LHC and $Z$ pole measurements are in agreement with the SM. This underscores the opportunities of a precision lepton collider to explore BSM quantum corrections to the Higgs sector more broadly.

Figures (4)

• Figure 1: Projections of the SFOEWPT scan as detailed in the main body of the text. Panel \ref{['fig:zst']} shows the compatibility with the $S$ and $T$ parameters at 68% CL (dotted blue line) and 95% CL (full blue line). Here, light grey points are parameter points compatible with the constraints specified in Sec. \ref{['sec:elwba']}, dark grey points additionally fulfil the SFOEWPT constraint $\xi_p >1$, and colored points fulfil the projected constraints on the EWPOs representatively obtained at a future FCC-ee for its $\sqrt{s}=m_Z$ phase. The $Z$-pole programme will efficiently single out a relatively small parameter space of the SFOEWPT-preferred parameter region. Panels \ref{['fig:zmass']} and \ref{['fig:zm']} show the contours of the allowed mass spectra after successively applying the constraints. Panel \ref{['fig:zlhc']} highlights the relation of this region in the context of the expected 125 GeV signal strength constraints obtainable at the HL-LHC at 68% CL (dotted red line) and 95% CL (dashed red line), displayed in the $\tan\beta$ versus $\cos(\beta-\alpha)$ plane.
• Figure 2: Interference-corrected (signal-signal as well as signal-background) cross sections compared to the pure signal process for LHC production of the uncharged heavy scalars, $H$ (blue points) and $A$ (red points), respectively, as a function of their respective mass, for the parameter points of the scan detailed in Sec. \ref{['sec:elwba']}.
• Figure 3: Feynman diagram toplogies contributing at NLO to $e^+ e^- \to hZ$ in the 2HDM. In particular, (b) and (d) are sensitive to Higgs-mixing effects. We omit $m_e\neq 0$ effects due to vanishingly small electron-Higgs couplings.
• Figure 4: Production of the SM-like Higgs boson in association with a $Z$ boson at the FCC-ee, in relation to the decoupling limit at $\sqrt{s}=240~\text{GeV}$ for the scan detailed in Sec. \ref{['sec:elwba']}. Blue points denote leading-order predictions, which are all compatible with the expected FCC-ee sensitivity of $hZ$ production of $\Delta \sigma/\sigma =0.31\%$Selvaggi:2025kmd; all points are compatible with an SM outcome of the FCC-ee $Z$-pole programme. Including radiative corrections (red points) modifies these predictions, creating the discovery potential at a lepton collider even when $Z$ pole observables are insensitive. The green region is the experimental sensitivity $\Delta \sigma/\sigma =0.31\%$. The decoupling cross section $\sigma_{\text{decoup}}$ is evaluated consistently at LO (blue points) and NLO (red points).