Strong First-Order Electroweak Phase Transitions and Gravitational Waves in the Normal Two-Higgs-Doublet Model: A Comparative Study of the Four Yukawa Types and Thermal Resummation Schemes

Author(s)

Cho, Jin-Hwan, Kim, Dongjoo, Kim, Jinheung, Lee, Soojin, Song, Jeonghyeon

Abstract

We present a comprehensive global analysis of strong first-order electroweak phase transitions (SFOEWPTs) and their associated stochastic gravitational-wave (GW) backgrounds within the Normal Scenario of the $CP$-conserving Two-Higgs-Doublet Model (2HDM) with softly broken $Z_2$ symmetry, where the lighter $CP$-even scalar is identified as the observed $125~\text{GeV}$ Higgs boson. Across all four Yukawa structures (Type-I, II, X, and Y), we track the finite-temperature vacuum evolution, transition dynamics, and GW signatures. To quantify the theoretical uncertainty associated with thermal resummation, we perform a detailed comparison between the Parwani and Arnold--Espinosa prescriptions. While both schemes find that single-step paths overwhelmingly dominate successful transitions and consistently favor the Higgs alignment limit, the resulting SFOEWPT parameter space exhibits a pronounced scheme dependence. The Arnold-Espinosa prescription severely restricts the viable parameter space (with upper bounds on the heavy-scalar masses below approximately 800 GeV) and introduces an extreme parametric sensitivity that produces fragmented distributions and irregular voids in the heavy-scalar mass planes. In contrast, the more stable Parwani prescription allows heavy-scalar masses below $\sim 1.6~\text{TeV}$. We further identify highly restricted GW parameter regions capable of yielding a four-year LISA signal-to-noise ratio above 10, while demonstrating that the acoustic GW source is generically short-lived, leading to a substantial suppression of the predicted signal amplitude. Our results highlight the strong complementarity between future space-based GW observations and high-energy collider searches in probing the cosmological viability of the 2HDM.

Figures

Distribution of SFOEWPT parameter points in the $(M_H, M_{H^\pm})$ plane for the single-step transition scenario in Type-I (upper panels) and Type-II (lower panels). The left and right panels compare results obtained using the Parwani and AE resummation schemes, respectively. The color scale denotes the order parameter $\xi_p$. The underlying gray points represent the initial physical parameter points satisfying all theoretical and experimental constraints. To highlight regions of stronger phase transitions, points with higher $\xi_p$ are plotted on top of those with lower values.
Caption Distribution of SFOEWPT parameter points in the $(M_H, M_{H^\pm})$ plane for the single-step transition scenario in Type-I (upper panels) and Type-II (lower panels). The left and right panels compare results obtained using the Parwani and AE resummation schemes, respectively. The color scale denotes the order parameter $\xi_p$. The underlying gray points represent the initial physical parameter points satisfying all theoretical and experimental constraints. To highlight regions of stronger phase transitions, points with higher $\xi_p$ are plotted on top of those with lower values.
Distribution of cosmologically viable parameter points in the $(M_H, M_{H^\pm})$ plane for the single-step transition scenario in Type-II under the AE resummation scheme, without applying the strong phase transition criterion $\xi_p>1$. The color scale denotes the order parameter $\xi_p$, and the underlying gray points represent the physical parameter points.
Caption Distribution of cosmologically viable parameter points in the $(M_H, M_{H^\pm})$ plane for the single-step transition scenario in Type-II under the AE resummation scheme, without applying the strong phase transition criterion $\xi_p>1$. The color scale denotes the order parameter $\xi_p$, and the underlying gray points represent the physical parameter points.
Distribution of SFOEWPT parameter points in the $(\Delta M_A, \Delta M_{H})$ plane for the single-step transition scenario in Type-I (upper panels) and Type-II (lower panels), where $\Delta M_i = M_i - M_{H^\pm}$. The left and right panels compare results obtained using the Parwani and AE resummation schemes, respectively. The color scale denotes the order parameter $\xi_p$. The underlying gray points represent the initial physical parameter points.
Caption Distribution of SFOEWPT parameter points in the $(\Delta M_A, \Delta M_{H})$ plane for the single-step transition scenario in Type-I (upper panels) and Type-II (lower panels), where $\Delta M_i = M_i - M_{H^\pm}$. The left and right panels compare results obtained using the Parwani and AE resummation schemes, respectively. The color scale denotes the order parameter $\xi_p$. The underlying gray points represent the initial physical parameter points.
Distribution of SFOEWPT parameter points in the $(|s_{\beta-\alpha}|, \tb)$ plane for the single-step transition scenario in Type-I (upper panels) and Type-II (lower panels). The left and right panels compare results obtained using the Parwani and AE resummation schemes, respectively. The color scale denotes the order parameter $\xi_p$.
Caption Distribution of SFOEWPT parameter points in the $(|s_{\beta-\alpha}|, \tb)$ plane for the single-step transition scenario in Type-I (upper panels) and Type-II (lower panels). The left and right panels compare results obtained using the Parwani and AE resummation schemes, respectively. The color scale denotes the order parameter $\xi_p$.
Distribution of the viable GW parameter points in the $(\beta_{\text{GW}}/H_*,\alpha_{\text{GW}})$ plane for the Type-I model under the Parwani (left panel) and AE (right panel) resummation schemes. The color scale denotes the four-year LISA signal-to-noise ratio.
Caption Distribution of the viable GW parameter points in the $(\beta_{\text{GW}}/H_*,\alpha_{\text{GW}})$ plane for the Type-I model under the Parwani (left panel) and AE (right panel) resummation schemes. The color scale denotes the four-year LISA signal-to-noise ratio.
Distribution of SFOEWPT parameter points in the $(M_H, M_A)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the phase transition order parameter $\xi_p$. The sub-panels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of SFOEWPT parameter points in the $(M_H, M_A)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the phase transition order parameter $\xi_p$. The sub-panels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Distribution of SFOEWPT parameter points in the $(M_{H^\pm}, \tb)$ plane for the single-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the order parameter $\xi_p$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of SFOEWPT parameter points in the $(M_{H^\pm}, \tb)$ plane for the single-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the order parameter $\xi_p$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Distribution of SFOEWPT parameter points in the $(s_{\beta-\alpha}, \tb)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the phase transition order parameter $\xi_p$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of SFOEWPT parameter points in the $(s_{\beta-\alpha}, \tb)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the phase transition order parameter $\xi_p$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Distribution of SFOEWPT parameter points in the $(\tb, m_{12}^2)$ plane for the single-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the order parameter $\xi_p$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of SFOEWPT parameter points in the $(\tb, m_{12}^2)$ plane for the single-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the order parameter $\xi_p$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Distribution of SFOEWPT parameter points for the second stage of the two-step SFOEWPT scenario ($\trans{2}{2}$) projected onto the $(M_H, M_A)$ plane (left panel) and the $(M_{H^\pm}, \tb)$ plane (right panel) for the Type-I model under the Parwani resummation scheme. The results are compiled from an expanded dataset totaling $5.4\times10^6$ baseline physical parameter points (gray points). The color scale denotes the order parameter $\xi_p$.
Caption Distribution of SFOEWPT parameter points for the second stage of the two-step SFOEWPT scenario ($\trans{2}{2}$) projected onto the $(M_H, M_A)$ plane (left panel) and the $(M_{H^\pm}, \tb)$ plane (right panel) for the Type-I model under the Parwani resummation scheme. The results are compiled from an expanded dataset totaling $5.4\times10^6$ baseline physical parameter points (gray points). The color scale denotes the order parameter $\xi_p$.
Distribution of viable GW parameter points ($\text{SNR}>10$) in the $(\xi_p,\text{SNR})$ plane for the Type-I 2HDM under the Parwani resummation scheme. The color scale denotes the supercooling measure $\zeta_{\rm SC}\equiv(T_c-T_n)/T_c$.
Caption Distribution of viable GW parameter points ($\text{SNR}>10$) in the $(\xi_p,\text{SNR})$ plane for the Type-I 2HDM under the Parwani resummation scheme. The color scale denotes the supercooling measure $\zeta_{\rm SC}\equiv(T_c-T_n)/T_c$.
Distribution of the SNR envelope parameter points projected onto the $(\xi_p, K_{\text{sw}}^2)$ plane (left panel) and the $(\xi_p, H_*/\beta_{\text{GW}})$ plane (right panel) for the Type-I 2HDM under the Parwani resummation scheme. The color scale denotes the four-year LISA $\text{SNR}$.
Caption Distribution of the SNR envelope parameter points projected onto the $(\xi_p, K_{\text{sw}}^2)$ plane (left panel) and the $(\xi_p, H_*/\beta_{\text{GW}})$ plane (right panel) for the Type-I 2HDM under the Parwani resummation scheme. The color scale denotes the four-year LISA $\text{SNR}$.
The sound-wave lifetime suppression factor $\Upsilon$ as a function of the percolation order parameter $\xi_p$ across the viable GW parameter space for the Type-I 2HDM under the Parwani resummation scheme. The color scale maps the corresponding supercooling measure $\zeta_\text{SC}$.
Caption The sound-wave lifetime suppression factor $\Upsilon$ as a function of the percolation order parameter $\xi_p$ across the viable GW parameter space for the Type-I 2HDM under the Parwani resummation scheme. The color scale maps the corresponding supercooling measure $\zeta_\text{SC}$.
Distribution of GW parameter points in the $(M_H, M_A)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the LISA four-year SNR. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of GW parameter points in the $(M_H, M_A)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the LISA four-year SNR. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Distribution of the viable GW parameter points in the $(M_{H^\pm}, \tb)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the LISA four-year $\text{SNR}$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of the viable GW parameter points in the $(M_{H^\pm}, \tb)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the LISA four-year $\text{SNR}$. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Distribution of GW parameter points in the $(s_{\beta-\alpha}, \tb)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the LISA four-year SNR. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
Caption Distribution of GW parameter points in the $(s_{\beta-\alpha}, \tb)$ plane for the one-step transition scenario across the four 2HDM types under the Parwani resummation scheme. The color scale denotes the LISA four-year SNR. The subpanels correspond to Type-I (upper left), Type-II (upper right), Type-X (lower left), and Type-Y (lower right).
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