⚛️ phenomenology

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

This paper investigates the UV viability of strongly first-order electroweak phase transitions in the Type-I 2HDM, revealing that while one-step transitions face a severe tension between transition strength and high-scale validity, multistep transitions in the Inverted Scenario can achieve both strong transitions and consistency up to the Planck scale, thereby favoring a light scalar spectrum and moderate $\tan\beta$ as a promising target for collider searches.

Original authors: Jin-Hwan Cho, Dongjoo Kim, Jinheung Kim, Jeonghyeon Song

Published 2026-09-10

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CC BY 4.0

Original authors: Jin-Hwan Cho, Dongjoo Kim, Jinheung Kim, Jeonghyeon Song

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the earliest moments of the universe, a fraction of a second after the Big Bang, the fundamental forces of nature were unified in a hot, chaotic soup. As the cosmos expanded and cooled, it underwent a profound transformation known as the electroweak phase transition. This event was akin to water freezing into ice, but instead of a smooth, gradual change, the universe needed to snap suddenly from a symmetric state into the broken symmetry we see today. For the universe to contain the matter we are made of, this snap had to be violent and abrupt, a "strongly first-order" transition that pushed the universe out of thermal equilibrium. Without this specific kind of violent shift, the delicate balance of matter and antimatter would have resulted in a universe filled only with radiation, leaving no room for stars, planets, or people.

Physicists have long known that the standard model of particle physics, which describes the known particles and forces, predicts a smooth transition rather than a violent snap. To explain the violent version required by the history of our universe, scientists look to theories that extend beyond the standard model. One of the most promising extensions involves adding extra Higgs fields, the invisible energy fields that give particles their mass. By introducing a second Higgs field, the universe could potentially undergo the necessary violent transition. However, for such a theory to be taken seriously, it must not only explain the past but also remain mathematically consistent as we look toward higher and higher energies, all the way up to the very limits of what we can describe with current physics.

A team of researchers has recently put this idea to a rigorous test, examining a specific version of this extended theory called the Type-I two-Higgs-doublet model. They asked a critical question: if the universe did undergo a violent phase transition in this specific way, how far could the laws of physics remain valid before they broke down? To answer this, they ran millions of computer simulations, scanning through a vast landscape of possible physical parameters. They looked for scenarios where the transition was strong enough to create the matter we see today, and then checked how high an energy scale these scenarios could survive before the mathematics of the theory began to fail. They found that the answer depends entirely on the "story" of how the transition happened.

The researchers discovered a sharp divide between two types of transition histories. In the most common scenario, the universe moves directly from the hot, symmetric state to the cold, broken state in a single, sudden step. In these one-step transitions, the team found a severe tension between the strength of the transition and the longevity of the theory. If the transition is made strong enough to satisfy the requirements for creating matter, the theory tends to break down at relatively low energy scales, roughly a million times the mass of a proton. Conversely, if the theory is forced to remain valid up to very high energies, the transition becomes too weak to explain the universe we inhabit. It is as if the theory has a strict budget: you can spend it on a strong transition or on high-energy stability, but you cannot have both in a single-step process.

However, the story changes dramatically when the transition happens in multiple steps. In this less common scenario, the universe pauses in a temporary, unstable state before finally settling into its current form. The researchers found that these multistep transitions, particularly those occurring in the "inverted" version of their model, behave in a completely different way. Here, the violent transition and the high-energy stability do not fight each other. The team identified scenarios where the transition was incredibly strong, far exceeding the minimum requirements, while the theory remained mathematically consistent up to energy scales trillions of times higher than what we can currently probe. These multistep events could theoretically survive all the way up to the grand unification scale, where the fundamental forces might merge into one.

This distinction has profound implications for what we should look for in future experiments. The study suggests that if nature chose the single-step path, we would likely see heavy new particles at current colliders, but the theory would struggle to explain the universe's high-energy history. If nature chose the multistep path, the new particles required to make this work would be much lighter, and the mixing between the different Higgs fields would be moderate. This points to a specific, narrow range of possibilities where the new particles could be light enough to be discovered by the High-Luminosity Large Hadron Collider or future machines like a multi-TeV muon collider. The researchers conclude that while the single-step path is crowded and constrained, the multistep path offers a promising, theoretically robust window into the physics of the early universe, waiting to be opened by the next generation of particle detectors.

Technical Summary: Cutoff Scales in the Type-I 2HDM with Strongly First-Order Electroweak Phase Transitions

Problem Statement
The paper investigates the ultraviolet (UV) viability of strongly first-order electroweak phase transitions (SFOEWPTs) within the Type-I two-Higgs-doublet model (2HDM). An SFOEWPT is a necessary condition for electroweak baryogenesis and a potential source of stochastic gravitational waves. While the Standard Model (SM) predicts a smooth crossover, extended Higgs sectors like the 2HDM can realize SFOEWPTs. A critical, yet largely unexplored, aspect of these scenarios is the cutoff scale ( $\Lambda_c$ ), defined as the highest energy scale at which the theory remains theoretically consistent (satisfying perturbativity, tree-level unitarity, and vacuum stability). The authors address how $\Lambda_c$ correlates with the transition strength ( $\xi_p$ ) and whether this relationship differs between one-step transitions and multistep transitions (involving intermediate metastable vacua). Specifically, they examine how imposing UV validity benchmarks ( $\Lambda_c > 1$ TeV and $\Lambda_c > 10$ TeV) constrains the viable parameter space, including Higgs masses and mixing angles, in both the Normal Scenario (NS, where $h_{125}$ is the lighter CP-even scalar) and the Inverted Scenario (IS, where $h_{125}$ is the heavier CP-even scalar).

Methodology
The authors perform a global analysis involving a scan of $5 \times 10^6$ physical parameter points for both the NS and IS.

Parameter Space: The scan covers the independent Type-I 2HDM parameters: $\tan\beta$ , $\sin(\beta-\alpha)$ , the soft-breaking mass parameter $m_{12}^2$ , and the masses of the BSM scalars ( $m_{\phi^0}$ , $M_A$ , $M_{H^\pm}$ ). Distinct scan ranges are used for NS and IS to reflect phenomenological constraints.
Constraints: Points are filtered for theoretical consistency (vacuum stability, boundedness from below, tree-level unitarity, perturbativity) and experimental constraints (electroweak oblique parameters $S, T, U$ , flavor physics, Higgs signal strengths, and direct searches) using 2HDMC and ScannerS interfaced with HiggsTools.
Phase Transition Analysis: The finite-temperature effective potential $V_{\text{eff}}$ is calculated using the Parwani resummation scheme for thermal daisy effects. The transition strength is characterized by the percolation order parameter $\xi_p = \Delta v(T_p)/T_p$ . SFOEWPTs are identified by $\xi_p > 1$ . Thermal histories are classified as one-step, two-step, or three-step.
UV Viability Analysis: For surviving SFOEWPT points, the authors determine $\Lambda_c$ using a two-loop renormalization-group equation (RGE) analysis via 2HDME. $\Lambda_c$ is defined as the minimum scale where perturbativity ( $|\lambda_i| < 4\pi$ ), tree-level unitarity (scattering eigenvalues $< 8\pi$ ), or vacuum stability is violated.

Key Contributions and Results
The study reveals a sharp qualitative distinction between one-step and multistep SFOEWPTs regarding their UV behavior:

One-Step Transitions (Dominant):
- Anticorrelation: There is a pronounced tension between transition strength and UV validity. The maximal $\xi_p$ decreases as the required $\Lambda_c$ increases.
- Quantitative Limits: Requiring $\Lambda_c > 10$ TeV restricts the transition strength to $\xi_p \lesssim 2.7$ in the NS and $\xi_p \lesssim 1.8$ in the IS. Conversely, requiring $\xi_p > 1$ limits the cutoff scale to $\Lambda_c \lesssim \mathcal{O}(10^6)$ GeV in both scenarios.
- Survival Rates: Only a small fraction of one-step points survive the $\Lambda_c > 10$ TeV requirement (0.12% in NS, 24.85% in IS).
- Parameter Constraints: In the NS, $\Lambda_c > 1$ TeV implies $M_H \lesssim 600$ GeV, $M_A \lesssim 680$ GeV, and $M_{H^\pm} \lesssim 700$ GeV. In the IS, the pseudoscalar mass is restricted to $M_A \in [190, 425]$ GeV, with a preference for lower masses as $\Lambda_c$ increases.
Multistep Transitions (Rare but Distinct):
- Absence of Anticorrelation: Unlike one-step transitions, multistep transitions do not exhibit the strong $\xi_p$ – $\Lambda_c$ anticorrelation.
- High UV Viability: Two-step SFOEWPTs, found primarily in the IS, can remain theoretically consistent up to $\Lambda_c \sim \mathcal{O}(10^{15})$ GeV while achieving strong transitions ( $\xi_p \simeq 7$ ) and substantial supercooling ( $\zeta_{SC} \simeq 0.7$ ).
- Parameter Space Reshaping: Imposing high cutoff scales on two-step IS scenarios significantly narrows the viable parameter space, favoring a light scalar spectrum ( $M_A \sim 100$ GeV, $m_h \sim 62.5\text{--}90$ GeV) and moderate $\tan\beta$ ( $2.8 \lesssim \tan\beta \lesssim 7.3$ for $\Lambda_c > 10^{13}$ GeV).

Significance
The paper establishes that the tension between strong phase transitions and high-scale UV validity is a characteristic feature of one-step thermal histories, not a generic property of all SFOEWPTs. The existence of multistep transitions (specifically two-step in the IS) that can sustain strong transitions ( $\xi_p \simeq 7$ ) up to GUT-scale cutoffs ( $\sim 10^{15}$ GeV) challenges the assumption that SFOEWPTs necessarily imply a low cutoff scale.

The authors conclude that imposing UV validity requirements sharpens the phenomenologically viable parameter space. In particular, the high-cutoff two-step SFOEWPT region in the Inverted Scenario, characterized by light BSM Higgs bosons and moderate $\tan\beta$ , presents a specific and promising target for current and future collider searches, including the HL-LHC, multi-TeV muon colliders, and the FCC-hh.

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