Conformal versus non-conformal two-Higgs-doublet model: phase transitions and gravitational waves

Abstract

In this work we investigate the CP-conserving two-Higgs-doublet model (2HDM) in two realizations: a classically conformal setup (C2HDM) and a non-conformal setup with explicit tree-level quadratic mass terms (NC2HDM). Imposing current theoretical and experimental constraints, we scan the parameter space and analyse the electroweak first-order phase-transition dynamics from the finite-temperature effective potential, determining the relevant thermodynamic scales and the associated parameters $α$ and $β/H_*$. In the resulting $(α, β/H_*)$ phase diagrams, the NC2HDM spans a substantially broader region and hosts the strongest transitions, whereas the C2HDM is confined to a nested, weaker-transition subset. This challenges the common expectation that classical conformal symmetry generically implies deep supercooling. By relaxing the Higgs-mass identification and varying the scalon mass, we show that sizable supercooling is obtained only when the radiative (one-loop) breaking of scale invariance is sufficiently mild, i.e. for a light scalon. We then compute the resulting stochastic gravitational-wave spectra and show that only the NC2HDM yields benchmark points potentially observable by future space-based interferometers such as LISA, TianQin and Taiji (and, in favourable cases, by more sensitive missions such as DECIGO/BBO).

Figures (7)

• Figure 1: Correlation between the PT strength $\alpha$ and the normalized inverse time PT duration $\beta/H_*$. Blue (orange) points correspond to the NC2HDM (C2HDM).
• Figure 2: The upper panels show the projection of the the parameter space on the plane covered by the masses $m_{H}$ and $m_A$ in the (N)C2HDM, while the lower panels show the projection on the plane $m_{H^\pm}-m_A$. The colour-bar legends show the value of the strength parameter $\alpha$.
• Figure 3: Correlation between quartic couplings in the (N)C2HDM. The upper panels show the correlation between $\lambda_1$ and $\lambda_2$, while the middle panels show the correlation between $\lambda_3$ and $\lambda_4$. Finally the lower panels show the correlation between $\lambda_5$ and $\lambda_{345}$. The colour-bar legends show the value of the strength parameter $\alpha$.
• Figure 4: The upper panels show the correlation between the critical temperature $T_c$ and the percolation temperature $T_p$ in the (N)C2HDM, while the lower panels show the correlation between $T_p$ and $v_p$, the position of the global minimum in the effective potential at $T=T_p$. The colour-bar legends show the value of the strength parameter $\alpha$.
• Figure 5: Impact of the scalon mass $m_h$ on the heavy scalar masses $m_H$ (indicated by the color bar), $m_A$ and $m_{H^\pm}$ in the C2HDM. The left, middle and right panels show the results for $m_h=35$ GeV, $m_h=125$ GeV, $m_h=215$ GeV, respectively. We can see that the smaller the scalon mass, the smaller the upper bounds on $m_H$, $m_A$ and $m_{H^\pm}$.