⚛️ phenomenology

Multi-Higgs production from a theory of varying Higgs quartic and top Yukawa couplings

This paper investigates the collider phenomenology of a model where the Higgs quartic and top Yukawa couplings are dynamically generated by two scalar fields, predicting distinct resonant signatures in multi-Higgs and top-quark pair production that can be constrained by current ATLAS data and further probed by the High-Luminosity LHC to test the dynamical origin of the electroweak sector.

Original authors: Ulf Danielsson, Rikard Enberg, Gunnar Ingelman, Soumyadip Kundu, Tanumoy Mandal, Subhadip Mitra

Published 2026-10-16

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CC BY 4.0

Original authors: Ulf Danielsson, Rikard Enberg, Gunnar Ingelman, Soumyadip Kundu, Tanumoy Mandal, Subhadip Mitra

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

For decades, physicists have wondered if the fundamental rules of the universe are truly fixed. We usually think of constants like the strength of gravity or the weight of an electron as unchanging numbers, set in stone since the beginning of time. However, some theories suggest these values might have shifted over the history of the cosmos, settling into their current values only as the universe cooled down. If this is true, the numbers we measure today are not arbitrary choices but the result of a dynamic process, much like a river finding its level after a storm. This idea is particularly intriguing when applied to the Higgs field, which gives particles their mass, and the top quark, the heaviest known particle. If the forces governing these two are not static but vary, it would imply that the very fabric of matter is more fluid than we imagined.

A team of researchers has now explored what this would look like if we could see it happening in a particle collider. They constructed a model where the strength of the Higgs interaction and the top quark interaction are not fixed numbers but are controlled by two invisible, heavy particles. These particles act as the levers that adjust the rules of the game. The researchers asked a simple question: if these levers exist, what would they leave behind if we smashed protons together at the highest energies we can achieve? They found that these invisible controllers would decay into pairs of Higgs bosons or pairs of top quarks, creating distinct signals that current experiments could potentially spot.

The study focuses on a scenario involving two distinct heavy particles, which the authors call a two-scalar theory. In this setup, one particle primarily influences the Higgs boson, while the other influences the top quark, though they can mix together. The researchers calculated how these particles would behave if they were created in the Large Hadron Collider. The outcome depends heavily on how heavy these new particles are. If they are relatively light, they tend to break apart into pairs of Higgs bosons. If they are heavier, crossing a specific energy threshold, they switch their preference and decay almost entirely into pairs of top quarks. This creates two very different signatures for scientists to look for: a burst of Higgs particles or a shower of top quarks.

The team calculated the likelihood of these events occurring and found that the rates could be significantly higher than what the standard laws of physics predict. For instance, the production of two Higgs bosons together could be many times more common than expected if these new particles exist. Even more striking is the prediction of events where three Higgs bosons are produced at once. In the standard model, this is an incredibly rare event, so rare that it is almost impossible to detect. However, in this new theory, the process could happen frequently enough to be seen with the upcoming High-Luminosity LHC, a future upgrade to the current collider that will collect vastly more data.

To test their ideas, the researchers looked at data already collected by the ATLAS experiment at the Large Hadron Collider. They searched for signs of these heavy particles in the existing records of Higgs pairs and top quark pairs. By comparing their theoretical predictions with the actual data, they were able to rule out certain combinations of particle masses and interaction strengths. They found that if these particles exist, they must be heavier than a certain limit or interact more weakly than previously hoped. Specifically, they established new boundaries on the energy scales where this new physics might hide, effectively narrowing the search area for future experiments.

The researchers also looked ahead to the High-Luminosity LHC, which is expected to operate with much greater intensity. They simulated what would happen if this machine ran for several years, gathering enough data to spot even the faintest signals. Their analysis suggests that a combination of different search strategies is essential. Looking only for Higgs pairs or only for top quark pairs would not be enough to fully understand the theory. Instead, scientists will need to combine measurements from both channels, along with the rare three-Higgs events, to piece together the full picture. This multi-channel approach offers a powerful way to determine if the forces governing the Higgs and the top quark are indeed dynamic, arising from a deeper, changing origin rather than being fixed constants of nature.

The work provides a clear roadmap for how to test these ideas. It shows that the universe might hold a secret where the rules of mass and interaction are not static but are the result of a dynamic process involving heavy, unseen particles. While the current data has not yet confirmed their existence, it has set the stage for a definitive test. If these particles are real, the next generation of collider data will likely reveal them through the distinct patterns of Higgs and top quark pairs they leave behind, offering a glimpse into a universe where the fundamental constants are alive and changing.

Technical Summary: Multi-Higgs Production from a Theory of Varying Higgs Quartic and Top Yukawa Couplings

Problem Statement
This paper investigates the collider phenomenology of a theoretical framework where dimensionless fundamental constants—specifically the Higgs quartic self-coupling ( $\lambda_h$ ) and the top-quark Yukawa coupling ( $\lambda_t$ )—are not fixed parameters but dynamically varying quantities. In this scenario, these couplings arise from the vacuum expectation values of heavy scalar fields. While previous work established a "One Scalar Theory" (1ST) where a single scalar governs both couplings, this study extends the framework to a "Two Scalar Theory" (2ST). In the 2ST, $\lambda_h$ and $\lambda_t$ are controlled by two distinct scalar fields ( $S_1$ and $S_2$ ) that can mix, generating physical mass eigenstates ( $\phi_1$ and $\phi_2$ ). The primary motivation is to determine if the electroweak sector has a dynamical origin by searching for deviations in rare Standard Model (SM) processes, particularly multi-Higgs production, which are highly suppressed in the SM but potentially enhanced in this model.

Methodology
The authors employ a bottom-up Effective Field Theory (EFT) approach. They promote the dimensionless couplings to spacetime-dependent functions, $\tilde{\lambda}_i = \lambda_i \epsilon_i(x)$ , where $\epsilon_i$ are dimensionless scalar fields. Through field redefinitions ( $\epsilon_i = \exp(S_i/\Lambda_i)$ ), they obtain canonically normalized real scalars ( $S_i$ ) that couple to the SM via dimension-five operators, with $\Lambda_i$ representing the characteristic new-physics energy scale.

The study focuses on two models:

One Scalar Theory (1ST): A single scalar $S_0$ governs both $\lambda_h$ and $\lambda_t$ .
Two Scalar Theory (2ST): Two scalars, $S_1$ and $S_2$ , independently control $\lambda_h$ and $\lambda_t$ . These fields mix via an angle $\alpha$ to form physical mass eigenstates $\phi_1$ and $\phi_2$ .

The authors utilize FeynRules to implement the interactions and generate Universal FeynRules Output (UFO) model files for MadGraph5_aMC@NLO. Cross-sections are calculated using NNPDF2.3 parton distribution functions (PDFs). For loop-induced processes (gluon-gluon fusion), analytical integrations are performed using Package-X, and higher-order QCD effects are accounted for using mass-dependent K-factors from Higlu to scale results to NNLO accuracy.

The analysis evaluates production mechanisms at the LHC ( $\sqrt{s} = 14$ TeV), including:

Inclusive gluon-gluon fusion ( $gg \to \phi_i$ ).
Associated production with a SM Higgs ( $gg \to h\phi_i$ ).
Associated production with top-quark pairs ( $pp \to t\bar{t}\phi_i$ ).

Decay branching ratios (BRs) are calculated for channels including $gg$, $\gamma\gamma$ , $hh$, $t\bar{t}$ , and multi-body decays ( $3h$ , $ht\bar{t}$ , $4h$ ). The authors assume the Narrow-Width Approximation (NWA) given the narrow widths of the scalars in the parameter space of interest.

Key Contributions and Results

Decay Dynamics and Kinematic Thresholds:
The paper establishes that the decay phenomenology is strictly kinematic. Below the di-top threshold ( $M_i < 2m_t$ ), the scalars decay predominantly into Higgs pairs ($hh$). Once the mass exceeds $2m_t$ , the partial width for $t\bar{t}$ scales linearly with mass ( $\Gamma_{t\bar{t}} \propto M_i$ ), while the $hh$ width is mass-suppressed ( $\Gamma_{hh} \propto M_i^{-1}$ ). Consequently, for $M_i > 2m_t$ , the branching ratio to $t\bar{t}$ rapidly approaches 100%, suppressing the di-Higgs signal.
Resonant and Associated Production:
- Resonant Di-Higgs ( $pp \to \phi_i \to hh$ ): The model predicts sizeable cross-sections for resonant $hh$ production, particularly in the intermediate mass window ( $2m_h < M_i < 2m_t$ ). For a benchmark scalar mass of 300 GeV, the di-Higgs rate can be enhanced by a factor of $\sim 12$ (for $\phi_1$ ) and $\sim 4$ (for $\phi_2$ ) relative to the SM prediction.
- Tri-Higgs Production ( $pp \to h\phi_i \to hhh$ ): A novel signature identified is the associated production of a heavy scalar with a SM Higgs, followed by the scalar's decay into two Higgses. This process yields a tri-Higgs final state. The authors find that for $M_1 = 300$ GeV, the cross-section is enhanced by a factor of $\sim 15$ over the tiny SM expectation ( $\sigma_{SM} \approx 0.1$ fb).
Experimental Constraints (ATLAS Recasting):
The authors recast recent 13 TeV ATLAS resonance searches for di-Higgs ( $b\bar{b}\gamma\gamma$ ) and di-top ( $t\bar{t}$ ) final states.
- They derive lower bounds on the effective new-physics scales $\Lambda_1$ and $\Lambda_2$ as functions of the scalar mass $M_i$ .
- The constraints are highly dependent on the mixing angle $\alpha$ and the specific channel. For instance, the di-Higgs channel primarily constrains $\Lambda_1$ (which governs the Higgs coupling), while the di-top channel constrains $\Lambda_2$ (governing the top coupling).
HL-LHC Projections:
The study projects the sensitivity of the High-Luminosity LHC (HL-LHC) with an integrated luminosity of $3000 \text{ fb}^{-1}$ .
- The analysis identifies regions of the parameter space ( $\Lambda_1, \Lambda_2, \alpha$ ) that are currently allowed but will be probed with $>2\sigma$ significance at the HL-LHC.
- Crucially, the authors demonstrate that the di-Higgs and di-top channels are complementary. The di-Higgs channel is sensitive to $\Lambda_1$ but largely insensitive to $\Lambda_2$ , whereas the di-top channel is sensitive to $\Lambda_2$ but insensitive to $\Lambda_1$ .
- Combined measurements of resonant $hh$, $t\bar{t}$ , and rare multi-Higgs topologies are required to fully test the parameter space and distinguish the dynamical origin of the couplings.

Significance
The paper claims that this framework provides a "strong, multi-channel test" of whether the electroweak sector has a dynamical origin. By moving beyond the minimal 1ST to the 2ST, the model introduces a richer phenomenology where the correlations between Higgs and top couplings are relaxed via mixing. The identification of the tri-Higgs ($hhh$) signature as a background-suppressed probe is a key finding, offering a distinct avenue for discovery that is otherwise inaccessible in the SM. The authors conclude that the HL-LHC, through combined analyses of multiple channels, has the potential to either discover these dynamical effects or place stringent bounds on the scales $\Lambda_1$ and $\Lambda_2$ , thereby testing the hypothesis that fundamental constants emerge from underlying scalar dynamics.

Technical Summary: Multi-Higgs Production from a Theory of Varying Higgs Quartic and Top Yukawa Couplings

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