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

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.