Cutoff Scales in the Type-I 2HDM with Strongly First-Order Electroweak Phase Transitions: One-Step versus Multistep

We investigate the UV viability of strongly first-order electroweak phase transitions (SFOEWPTs) in the Type-I two-Higgs-doublet model (2HDM), considering both the Normal and Inverted Scenarios (NS and IS). For each scenario, we scan $5\times {10}^6$ physical parameter points and determine the cutoff scale ${\mathrm{\Lambda }}_{\mathrm{c}}$ through a two-loop renormalization-group analysis, where ${\mathrm{\Lambda }}_{\mathrm{c}}$ is set by the first violation of perturbativity, tree-level unitarity, or vacuum stability. For one-step transitions, the SFOEWPT strength and high-scale UV validity exhibit a pronounced tension: the maximal transition strength ${\xi }_p$ decreases with increasing ${\mathrm{\Lambda }}_{\mathrm{c}}$. Requiring ${\mathrm{\Lambda }}_{\mathrm{c}}>10\text{ TeV}$ limits the transition strength to ${\xi }_p\lesssim 2.7$ in the NS and ${\xi }_p\lesssim 1.8$ in the IS, while requiring ${\xi }_p>1$ restricts the cutoff scale to ${\mathrm{\Lambda }}_{\mathrm{c}}\lesssim O({10}^6)\text{ GeV}$ in both scenarios. Multistep transitions exhibit qualitatively different behavior. Two-step SFOEWPTs, found in appreciable numbers only in the IS, can remain theoretically consistent up to ${\mathrm{\Lambda }}_{\mathrm{c}}\sim O({10}^{15})\text{ GeV}$ while reaching ${\xi }_p\simeq 7$, without exhibiting the pronounced ${\xi }_p$-${\mathrm{\Lambda }}_{\mathrm{c}}$ anticorrelation characteristic of one-step transitions. Imposing UV validity also sharpens the phenomenologically viable parameter space. In particular, increasing the minimum allowed cutoff scale for two-step SFOEWPTs in the IS favors a light scalar spectrum and moderate $\tan \beta$, providing a promising target for current and future collider searches.