⚛️ phenomenology

Production of dark matter in association with a Higgs boson via exclusive photon fusion in $pp$ collisions at $\sqrt{s}=13$ TeV

This paper investigates the production of dark matter in association with a Higgs boson via central exclusive photon fusion in 13 TeV proton-proton collisions within the Inert Doublet Model plus a complex Singlet framework, demonstrating how forward proton detectors at the LHC can be used to search for this Beyond the Standard Model process by analyzing the missing mass spectrum for various mass differences.

Original authors: M. A. Arroyo-Ureña, H. Hernández-Arellano, I. Pedraza, S. Rosado-Navarro, T. A. Valencia-Pérez

Published 2026-02-24

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CC BY 4.0

Original authors: M. A. Arroyo-Ureña, H. Hernández-Arellano, I. Pedraza, S. Rosado-Navarro, T. A. Valencia-Pérez

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

Imagine the universe is a giant, bustling party. We know most of the guests (the atoms, stars, and planets we can see), but there's a huge, invisible crowd in the corner that we can't see or touch. We only know they are there because they are pulling on the furniture with invisible strings (gravity). This invisible crowd is Dark Matter.

Physicists have been trying to figure out what these invisible guests look like. This paper is a proposal for a new way to catch a glimpse of them at the world's biggest particle collider, the Large Hadron Collider (LHC).

Here is the story of their idea, broken down into simple concepts:

1. The "Invisible Guest" and the "Party Hat"

The authors propose a new theory called the IDMS (Inert Doublet Model plus a Singlet).

The Dark Matter Candidate ( $\chi$ ): Think of this as a very shy, invisible guest who never leaves the party. They are so shy that they don't talk to anyone (they don't interact with light or normal matter easily).
The Higgs Boson ( $h$ ): Imagine this as a famous celebrity at the party. Everyone knows them, and they interact with almost everything.
The Heavy Scalar ( $S$ ): This is the "matchmaker" or the "bouncer." It's a heavy, invisible particle that can turn into the celebrity (Higgs) and the shy guest (Dark Matter) all at once.

2. The "Exclusive VIP Lounge" (Central Exclusive Production)

Usually, when two protons (the main guests) crash into each other at the LHC, it's like a mosh pit. Everything gets smashed, debris flies everywhere, and it's very messy. It's hard to spot a specific invisible guest in that chaos.

But this paper suggests a different scenario: Exclusive Photon Fusion.

Imagine two protons approaching each other but not crashing head-on. Instead, they are like two polite dancers who pass each other very closely.
As they pass, they exchange a "glance" (a photon). This exchange is so gentle that the protons don't break apart; they just get a little push and keep walking away, still intact.
Because they didn't crash, the "dance floor" (the center of the collision) is very clean. In the middle, that "glance" creates the Heavy Scalar ( $S$ ), which immediately splits into the Higgs (celebrity) and the Dark Matter (shy guest).

3. The "Missing Mass" Trick

How do we know the Dark Matter was there if we can't see it?

The two protons that passed by are caught by special detectors at the very edge of the tunnel (like security cameras at the exit).
Scientists measure exactly how much energy those protons lost during their "glance."
The Analogy: Imagine you see two people walk past a window. You know exactly how much energy they had before. If you see them walk away with slightly less energy, you know something happened in the middle.
If the math says, "The protons lost 100 units of energy," and the Higgs boson we see only accounts for 60 units, then 40 units are missing. That missing energy must be the Dark Matter! This is called the Missing Mass technique.

4. The "Safety Rules" (Stability)

A big problem with these theories is: Why doesn't the Dark Matter just decay into normal stuff and disappear?

The authors set up a "Safety Rule" (a kinematic condition). They ensure the Heavy Scalar ( $S$ ) is heavy enough to split into the Higgs and Dark Matter, but the Dark Matter itself is the lightest, most stable particle in its family.
It's like a heavy box that can only be opened to reveal a lighter box and a feather. Once the feather is out, it can't break down any further. This ensures the Dark Matter stays around forever.

5. What Did They Find?

The team ran computer simulations to see if this "polite dance" could actually happen and be detected.

The Results: They found that if the "matchmaker" particle ( $S$ ) is heavy enough and the energy gap is just right, this process can happen.
The Catch: The signal is rare. It's like trying to spot a specific shy guest at a party of a billion people.
The Good News: Because the protons stay intact, the "background noise" (the messy debris from normal crashes) is almost zero. This makes the signal much cleaner and easier to spot than in a mosh-pit collision.

The Bottom Line

This paper is a blueprint for a new kind of treasure hunt. Instead of smashing protons to pieces to find Dark Matter, the authors suggest watching them gently pass each other. If the protons lose a tiny bit of energy and we see a Higgs boson appear, we might finally catch a glimpse of the invisible Dark Matter guest, proving it exists and telling us what it weighs.

It's a clever, clean, and promising way to look for the universe's biggest mystery.

1. Problem Statement

The nature of Dark Matter (DM) remains one of the most significant unsolved problems in cosmology and particle physics. While indirect and direct detection methods exist, collider searches offer a unique pathway to probe DM interactions.

The Challenge: Standard collider searches for DM typically rely on "mono-X" signatures (missing transverse energy + a visible particle), which suffer from large Standard Model (SM) backgrounds.
The Specific Gap: There is a need to explore alternative production mechanisms that offer cleaner experimental signatures. Specifically, this paper investigates the production of a DM particle ( $\chi$ ) in association with a Higgs boson ( $h$ ) via Central Exclusive Production (CEP) initiated by photon fusion ( $pp \to p + \gamma\gamma \to p + S + p$ ).
The Model: The study utilizes the Inert Doublet Model plus a complex Singlet (IDMS). This extends the SM with an additional $U(1)_X$ gauge symmetry and an inert $SU(2)$ scalar doublet ( $\Phi_2$ ), providing a stable DM candidate.

2. Methodology

Theoretical Framework (IDMS)

The authors construct a model extending the SM gauge group $G_{SM} \times U(1)_X$ .

Scalar Sector: Includes the SM Higgs doublet ( $\Phi_1$ ), an inert doublet ( $\Phi_2$ ), and a complex singlet ( $S_X$ ).
Stability Mechanism: The stability of the DM candidate ( $\chi$ $χ$ , the lightest neutral component of $\Phi_2$ $Φ_{2}$ ) is ensured by either:
1. A discrete $Z_2$ symmetry (where $\Phi_2 \to -\Phi_2$ ).
2. The $U(1)_X$ gauge symmetry (by assigning specific charges such that decay terms are forbidden).
Symmetry Breaking: The singlet $S_X$ breaks the $U(1)_X$ symmetry, while $\Phi_1$ breaks the electroweak symmetry.
Kinematics: The process of interest is $pp \to p(\gamma\gamma \to S)p \to p(h\chi)p$ . A critical kinematic condition is imposed: $\Delta = M_S - M_\chi - M_h > 0$ . This ensures the heavy scalar $S$ can decay into the Higgs and DM, while preventing the DM from decaying further (ensuring stability).

Computational Tools

Model Implementation: The IDMS was implemented using LanHEP to generate UFO files.
Cross-Section Calculation: MadGraph5 was used to calculate the production cross-sections for the exclusive photon-fusion process at $\sqrt{s} = 13$ TeV.
Phenomenological Constraints:
- Relic Density: Calculated using MicrOMEGAs and constrained to the Planck value ( $\Omega h^2 = 0.1200 \pm 0.0012$ ).
- Direct Detection: Constraints from the LUX-ZEPLIN (LZ) experiment were applied to the spin-independent DM-nucleon scattering cross-section.
- Collider Limits: Results were compared against recent CMS searches for DM associated with a Higgs boson decaying to $b\bar{b}$ .

3. Key Contributions

Exclusive Photon Fusion in IDMS: The paper is the first to analyze the specific CEP channel ( $pp \to p(h\chi)p$ ) within the IDMS framework. This mechanism is distinct from standard gluon-fusion or $Z'$ -mediated production.
Stability Analysis: The authors rigorously demonstrate how the interplay between the $U(1)_X$ gauge symmetry and the kinematic condition $\Delta > 0$ ensures the stability of the DM candidate, even in the presence of potentially dangerous couplings like $\lambda_{12x}$ .
Parameter Space Scanning: A comprehensive scan was performed over the model parameters ( $v_x, \lambda_{1,2,3,4,5}, \lambda_{2x}, \lambda_{12x}$ $v_{x}, λ_{1, 2, 3, 4, 5}, λ_{2 x}, λ_{12 x}$ ) to identify benchmark points that satisfy:
- Planck relic density constraints.
- LUX-ZEPLIN direct detection limits.
- Perturbativity and theoretical consistency.
Experimental Signature Definition: The study highlights the unique signature of this process: two intact forward protons (detectable by near-beam spectrometers like CT-PPS or AFP) and a central system with missing mass, offering a background-free environment compared to inclusive searches.

4. Results

Cross-Section Behavior:
- The production cross-section ( $\sigma$ ) increases monotonically with the coupling $g_{Sh\chi}$ and the phase space $\Delta$ .
- Conversely, $\sigma$ decreases as the heavy scalar mass $M_S$ increases due to phase-space suppression.
- Calculations were performed for $M_S \in [800, 1800]$ GeV and $\Delta \in [20, 50]$ GeV.
Parameter Constraints:
- Direct Detection: The LUX-ZEPLIN limits impose strict constraints on the coupling $\lambda_{2x}$ , particularly for large vacuum expectation values ( $v_x \sim 30$ TeV), restricting $\lambda_{2x}$ to $\mathcal{O}(10^{-2})$ .
- Relic Density: For the chosen mass ranges, the IDMS model alone often under-produces the relic density, suggesting the need for additional sources or specific parameter tuning to match the Planck value.
Viability Against Collider Limits:
- When compared to CMS exclusion limits (searching for $h \to b\bar{b} + \text{MET}$ ), a significant portion of the benchmark parameter space remains viable.
- The exclusive photon fusion channel is not fully constrained by current inclusive CMS searches because the forward proton requirement and the specific kinematics of the CEP process differ significantly.
- Viable regions exist where the coupling $g_{Sh\chi} \sim 10^{-3}$ .

5. Significance and Outlook

Complementary Search Strategy: This work demonstrates that Central Exclusive Production via photon fusion is a powerful, complementary tool for DM searches. It offers a "clean" signature with low SM background, accessible via forward proton detectors (CT-PPS, AFP) at the LHC.
Model Validation: The IDMS framework remains a robust candidate for DM physics, capable of satisfying cosmological and direct detection constraints while predicting observable signals at the LHC.
Future Prospects: The authors conclude that with higher luminosity runs and improved forward detector performance, the missing mass spectrum in the CEP channel could either constrain the IDMS parameters further or lead to the discovery of this specific DM-Higgs production mode. A full detector-level simulation including background estimation is recommended for future work to quantify the discovery potential.

In summary, the paper provides a rigorous theoretical and phenomenological case for searching for Dark Matter in association with a Higgs boson through exclusive photon fusion, identifying viable parameter spaces that survive current experimental limits and proposing a distinct experimental strategy for the LHC.