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

Abstract

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 $5\times10^6$ physical parameter points and determine the cutoff scale $Λ_{\rm c}$ through a two-loop renormalization-group analysis, where $Λ_{\rm c}$ 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 $ξ_p$ decreases with increasing $Λ_{\rm c}$. Requiring $Λ_{\rm c}>10~\text{TeV}$ limits the transition strength to $ξ_p\lesssim2.7$ in the NS and $ξ_p\lesssim1.8$ in the IS, while requiring $ξ_p>1$ restricts the cutoff scale to $Λ_{\rm c}\lesssim O(10^6)~\text{GeV}$ 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 $Λ_{\rm c}\sim O(10^{15})~\text{GeV}$ while reaching $ξ_p\simeq7$, without exhibiting the pronounced $ξ_p$-$Λ_{\rm c}$ 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 $\tanβ$, providing a promising target for current and future collider searches.