⚛️ phenomenology

When the HL-LHC is blind, LISA is deaf (but not vice versa): 2HDM collider-cosmology synergies

This paper demonstrates that in the CP-conserving type-I 2HDM, the parameter space capable of producing a gravitational wave signal detectable by LISA is almost entirely constrained by future HL-LHC searches for heavy Higgs decays, establishing a strong synergy where collider data can rule out LISA-detectable scenarios, though a collider discovery does not guarantee a gravitational wave signal due to theoretical uncertainties and parameter tuning.

Original authors: Stefano Moretti, André Pousette, Carlo Tasillo

Published 2026-08-26

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CC BY 4.0

Original authors: Stefano Moretti, André Pousette, Carlo Tasillo

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

The universe began in a state of extreme heat and density, a primordial soup where the fundamental forces of nature were unified. As this cosmic fireball expanded and cooled, it underwent a profound transformation known as the electroweak phase transition. Imagine the water in a pot on a stove: as it cools, it can suddenly freeze into ice, releasing energy and changing its structure. In the early universe, a similar shift occurred when the Higgs field, which gives particles their mass, settled into its current state. In the simplest version of our physical laws, this change was smooth and gradual, like water turning into ice so slowly that no bubbles form. However, many physicists suspect the transition was actually violent and abrupt, like water boiling over. If it was, the collision of bubbles in the early universe would have created ripples in space-time itself, known as gravitational waves. These ripples would still be traveling through the cosmos today, carrying a secret message about the first moments of existence.

For decades, scientists have searched for these ancient ripples, but they have remained elusive. Now, a new study offers a way to catch them, not just by listening to the universe, but by looking at it with our most powerful particle colliders. The researchers focused on a specific extension of our standard model of physics called the two-Higgs-doublet model. This theory suggests that the universe contains not just one Higgs particle, but a whole family of them, including heavier, invisible cousins. The team set out to determine if these extra particles could trigger the violent phase transition needed to create detectable gravitational waves, and whether we could find them before the waves arrive.

The study combined two very different ways of exploring the universe: the high-energy collisions of the Large Hadron Collider (LHC) and the future space-based gravitational wave observatory known as LISA. The researchers ran millions of computer simulations, scanning through a vast landscape of possible masses and interactions for these extra Higgs particles. They were looking for a specific sweet spot where the physics would allow for a strong, violent phase transition that generates a loud gravitational wave signal. What they found was a striking pattern. The only regions where the universe would have produced a loud enough signal for LISA to hear were the exact same regions where the upgraded LHC, known as the High-Luminosity LHC, would be able to see the extra particles directly.

The researchers identified two distinct "clouds" of possibilities within the theory. In one scenario, called the standard-custodial cloud, the extra particles have masses that make them nearly identical to each other in a specific way. In this scenario, the gravitational waves are loud enough to be detected by LISA, but only if the heavy Higgs particles have masses between 180 and 250 GeV. Crucially, the study found that 95 percent of these specific scenarios would already be discovered by the High-Luminosity LHC through a specific decay channel where the heavy particle splits into two Z bosons, which then decay into four leptons. In the second scenario, the twisted-custodial cloud, the particles are arranged differently, and the gravitational waves are much quieter, likely too faint for LISA to hear. However, even in this quieter case, the particles would still be visible to the LHC.

The paper also addressed a previous claim in the scientific community that suggested these gravitational waves could be incredibly loud, far louder than what this new study predicts. The authors carefully analyzed why those earlier predictions were likely incorrect, showing that they relied on mathematical shortcuts that break down under closer inspection. They demonstrated that the signal strength is limited by the physical size of the bubbles forming in the early universe, preventing the signal from becoming arbitrarily loud. This correction brings the theoretical predictions down to a more realistic level, reinforcing the idea that the gravitational waves will be faint but detectable, provided the extra particles exist in the specific mass range the LHC can probe.

The most significant conclusion of this work is the deep connection between the two types of experiments. If the High-Luminosity LHC searches for these heavy particles and finds nothing in the mass range of 180 to 250 GeV, it effectively rules out the possibility that LISA will ever hear the gravitational waves from this specific type of phase transition. The collider acts as a gatekeeper; if it cannot see the particles, the universe did not make the loud sound we were hoping for. Conversely, if the LHC does find these particles, it would provide a strong reason for LISA to listen carefully, as the discovery would confirm that the conditions for a loud signal are met. This creates a powerful synergy where the particle collider and the gravitational wave detector are not competing, but working together to solve the same mystery.

The researchers were careful to note that while they are confident the LHC can test these scenarios, the exact loudness of the gravitational waves depends on some theoretical details that are still being refined. However, the core finding remains robust: the parts of the theory that produce the loudest signals are the same parts that the LHC can test most easily. This means that the next generation of particle physics experiments will likely determine whether we will ever hear the echo of the universe's birth from this specific source. If the LHC comes up empty in the coming years, the search for these particular gravitational waves may need to be abandoned, saving the world's most sensitive listening devices from a fruitless search. If, however, the LHC finds a new particle, it will be a signal to the world to tune in, as the universe may be about to whisper its earliest secrets.

Technical Summary: "When the HL-LHC is blind, LISA is deaf (but not vice versa): 2HDM collider-cosmology synergies"

Problem and Motivation
The Standard Model (SM) fails to explain the observed matter-antimatter asymmetry of the universe, as the SM electroweak phase transition (EWPT) is a smooth crossover rather than a strong first-order transition (SFOEWPT) required for electroweak baryogenesis. Extensions of the scalar sector, such as the Two-Higgs-Doublet Model (2HDM), can induce a SFOEWPT, generating a stochastic gravitational wave (GW) background potentially detectable by the Laser Interferometer Space Antenna (LISA). However, comprehensive scans of the 2HDM parameter space suggest that such strong transitions are rare and often rely on delicate cancellations. Furthermore, the interplay between collider constraints (specifically from the High-Luminosity LHC, HL-LHC) and GW observability remains to be systematically quantified. This work investigates whether regions of the CP-conserving type-I 2HDM that produce observable GW signals at LISA are simultaneously testable at the HL-LHC, and conversely, whether HL-LHC null results would preclude LISA discoveries.

Methodology
The authors perform an extensive exploration of the viable parameter space of the CP-conserving type-I 2HDM using a dual approach:

Parameter Space Scanning: A combination of a uniform random scan ( $10^4$ points) and a targeted Markov Chain Monte Carlo (MCMC) scan using the EMCEE algorithm. The MCMC is designed to maximize the LISA signal-to-noise ratio (SNR), defined as $p(x) \propto \text{SNR}^2(x)$ .
Theoretical Framework: The finite-temperature effective potential is computed up to one-loop order with Daisy resummation (Arnold-Espinosa prescription). The analysis utilizes two independent codes, BSMPT v3 and TransitionListener v2 (TL), to compute the phase transition history and GW spectra. This cross-validation serves to estimate theoretical uncertainties regarding the effective potential, bubble nucleation, and GW signal modeling (specifically sound-wave lifetime and wall velocity).
Constraints: The parameter space is constrained by theoretical requirements (boundedness from below, vacuum stability, perturbative unitarity) and observational limits (electroweak precision observables $S, T, U$ , flavor constraints, and direct searches for additional scalars at LEP, Tevatron, and LHC via HiggsBounds and HiggsSignals).
Collider Projections: The study projects HL-LHC sensitivity ( $\sqrt{s}=14$ TeV, $3 \text{ ab}^{-1}$ ) by rescaling current ATLAS and CMS limits. Key channels include $H \to ZZ$ , $H \to WW$ , $H \to \tau\tau$ , $H \to hh$ , $A \to Zh$ , and charged Higgs decays.
GW Calculation: The GW spectrum is modeled as the sum of sound wave and turbulence contributions. The detectability is assessed via the SNR at LISA, considering different observation times (3 yr for BSMPT, 4 yr for TL) and noise models (with and without astrophysical foregrounds).

Key Contributions and Results
The analysis identifies two distinct, narrow regions in the 2HDM parameter space ("clouds") where SFOEWPTs occur, driven by the need to satisfy electroweak precision constraints (specifically the $\rho$ parameter) while maintaining a strong transition:

Standard-Custodial Cloud: Characterized by the near-degeneracy $m_A \simeq m_{H^\pm}$ .
- Mass Ranges: $m_H \simeq 180\text{--}250$ GeV, $m_A \simeq 410\text{--}431$ GeV, $m_{H^\pm} \simeq 420\text{--}437$ GeV.
- GW Signal: This region produces the strongest signals, with maximal SNR values reaching $\sim 141$ (BSMPT) and $\sim 56$ (TL) for the most optimistic points.
- Collider Testability: Crucially, 94.8% to 95.9% of the points in this cloud that yield an observable LISA signal (SNR > 10) are already within the projected reach of the HL-LHC. The dominant probe is the resonant $gg \to H \to ZZ$ channel. The heavy CP-even scalar $H$ in this mass range couples sufficiently to the SM gauge bosons to be detected.
- Mechanism: The strong transition is driven by a large negative $\lambda_5$ (non-decoupling pseudoscalar $A$ ) and a specific realization of custodial symmetry ( $\lambda_4 \simeq \lambda_5$ ). The barrier is primarily generated by the zero-temperature one-loop Coleman-Weinberg term, not thermal effects.
Twisted-Custodial Cloud: Characterized by the near-degeneracy $m_H \simeq m_{H^\pm}$ .
- Mass Ranges: $m_H \simeq 170\text{--}200$ GeV, $m_A \simeq 560\text{--}580$ GeV.
- GW Signal: Transitions here are systematically weaker ( $\alpha \simeq 0.07\text{--}0.12$ ) due to higher percolation temperatures. The SNR generally stays below the LISA detection threshold (SNR > 10), with only a handful of points marginally crossing SNR > 1 in optimistic scenarios.
- Collider Testability: Despite the weak GW signals, this cloud is ~100% testable at the HL-LHC via the $H \to ZZ$ channel, as the light $H$ mass ( $\sim 170\text{--}200$ GeV) falls squarely in the resonance region with high production cross-sections.

Significance and Claims
The paper establishes a decisive complementarity between collider and GW probes in the context of the type-I 2HDM:

"When the HL-LHC is blind, LISA is deaf": If the HL-LHC excludes the $H \to ZZ$ signal in the mass window $m_H \simeq 180\text{--}250$ GeV (standard-custodial cloud), it effectively rules out the possibility of a detectable GW background from a strong EWPT in the 2HDM. The parameter space required for a loud GW signal is almost entirely covered by collider sensitivity.
"But not vice versa": A discovery of new scalars at the HL-LHC (e.g., an excess in $H \to ZZ$ ) does not guarantee a GW detection. The specific parameter tuning required to achieve a strong first-order transition (and thus a loud GW signal) is a subset of the collider-allowed region. Therefore, collider discovery alone cannot confirm the order or strength of the phase transition necessary for baryogenesis; LISA observations would still be required.
Robustness: The authors argue that their conclusions are robust against theoretical uncertainties. While the absolute SNR values vary significantly between BSMPT and TL (due to differences in sound-wave lifetime modeling and observation time conventions), the fraction of LISA-observable points that are also collider-testable remains stable ( $\sim 95\%$ ).
Correction of Literature: The study disputes previous claims (e.g., Ref. [21]) of extremely high SNRs ( $\sim 10^8$ ) in the 2HDM. The authors attribute such values to the use of the bounce-action slope $(\beta/H)_S$ which can vanish or become negative for slow transitions, leading to unphysical bubble separations exceeding the Hubble radius. Using the mean bubble separation at percolation $(\beta/H)_{R_H}$ , the authors find maximal SNRs orders of magnitude lower.

In summary, the work demonstrates that for the type-I 2HDM, the search for strong EWPTs via GWs is not a "blind" search independent of colliders; rather, the HL-LHC acts as a powerful filter, capable of testing the vast majority of the parameter space that would otherwise be visible to LISA.

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