⚛️ phenomenology

Monojet and direct detection constraints on real scalar dark matter: EFT and a simple UV completion

This paper analyzes constraints on real scalar dark matter by comparing LHC monojet searches with direct detection limits using both an effective field theory approach and a specific UV completion involving vector-like quarks, identifying parameter regions where collider data provides crucial complementary bounds.

Original authors: Arnab Roy, Michael A. Schmidt, German Valencia

Published 2026-02-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Arnab Roy, Michael A. Schmidt, German Valencia

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, invisible puzzle. We know most of the pieces (stars, planets, you, me), but about 85% of the puzzle is missing. We call this missing piece Dark Matter. We can't see it, but we know it's there because of how it pulls on things with gravity.

This paper is like two detectives trying to figure out what this missing piece looks like, using two different magnifying glasses.

The Two Detectives: The "EFT" and the "UV Model"

The authors are studying a specific theory where Dark Matter is a simple, invisible ball (a "real scalar"). To find it, they use two different approaches:

The "Effective Field Theory" (EFT) Detective:
- The Analogy: Imagine you are trying to understand a complex machine, but you can only see the outside. You don't know how the gears inside work, so you just write down a rule: "If you push the button hard enough, the machine shakes."
- In the paper: This approach treats the heavy particles that might carry the Dark Matter as if they are infinitely heavy and invisible. It uses a "black box" formula to guess how Dark Matter interacts with normal matter. It's a great shortcut, but it breaks down if you push the machine too hard.
The "UV Completion" (The Full Blueprint) Detective:
- The Analogy: This detective gets to open the machine. They see the actual gears, springs, and levers (called Vector-Like Quarks). They know exactly how the machine works, including what happens when you push the button really, really hard.
- In the paper: This is a specific, complete theory where Dark Matter is created by heavy, new particles that decay into a jet of normal particles and the invisible Dark Matter ball.

The Experiment: The "Monojet" Hunt

How do they look for this invisible ball? They use the Large Hadron Collider (LHC), a giant particle smasher.

The Setup: They smash protons together.
The Clue: Sometimes, a collision creates a single, high-speed jet of particles (a "Monojet") that flies off in one direction, while the rest of the energy just... disappears.
The Metaphor: Imagine two cars crashing in a dark room. If you see one car fly off to the left at high speed, but the room stays dark and quiet, you know something invisible must have been hit and flown off to the right. That "missing energy" is the Dark Matter.

The Big Discovery: The Magnifying Glasses Don't Always Match

The authors compared the results from the "Shortcut Detective" (EFT) and the "Full Blueprint Detective" (UV Model). Here is what they found:

1. The "High-Speed" Trap
The Shortcut Detective (EFT) works great when the collision is gentle. But when the collision gets very energetic (high energy), the shortcut breaks.

The Analogy: It's like using a map of a city that only shows streets up to 50 mph. If you drive at 150 mph, the map says you'll hit a wall, but in reality, there's a highway ramp you didn't know about.
The Result: The "Full Blueprint" model showed that at high energies, the heavy new particles can actually be created on purpose (like a resonance), creating a spike in the data that the Shortcut model completely missed.

2. The "Scale" Confusion
The authors found that the computer programs used to simulate these crashes were using different "rulers" (scales) for the two models.

The Analogy: Imagine measuring a room with a tape measure for one model and a laser for the other. Even if you measure the same room, the numbers look different because the tools are calibrated differently.
The Fix: They realized that if they forced both detectives to use the exact same ruler, the results matched much better at lower energies.

3. The "Flawed" Data Point
There was one specific data bin (a specific range of missing energy) where the real-world data from the LHC looked a bit weird (a statistical fluctuation).

The Result: The Shortcut model (EFT) got confused by this weird data and started excluding "normal" physics (the Standard Model) as if it were wrong. The Full Blueprint model was more robust and realized, "Hey, that's just a fluke; the normal physics is still fine."

The Second Detective: The "Direct Detection"

While the LHC is like smashing things to create Dark Matter, Direct Detection experiments (like PandaX or LZ) are like setting a trap to catch Dark Matter that is already floating around in space.

The Analogy: The LHC is a factory trying to build a new toy. Direct Detection is a fisherman trying to catch a fish that's already in the lake.
The Finding: Usually, the fisherman (Direct Detection) is much better at catching the fish. However, the authors found a few special "holes" in the fisherman's net where the fish could slip through. In those specific holes, the factory (LHC Monojet search) is actually the only one who can catch the fish!

The Bottom Line

This paper is a warning and a guide for physicists:

Don't trust the shortcut blindly: Using the "Effective Field Theory" (the shortcut) to analyze high-energy data can lead you to wrong conclusions, especially if new heavy particles exist just beyond our current reach.
Check your tools: Make sure your computer simulations are using the same "rulers" when comparing different theories.
Teamwork is key: You need both the "Factory" (LHC) and the "Fisherman" (Direct Detection) working together. Sometimes the fisherman misses the fish, and only the factory can find it, and vice versa.

In short, they showed us that while the "shortcut" is useful, we need to be careful not to drive too fast with it, or we might crash into a reality we didn't expect!

1. Problem Statement

The paper addresses the limitations of using Effective Field Theories (EFTs) to constrain Dark Matter (DM) models, specifically in the context of monojet searches at the Large Hadron Collider (LHC).

The Issue: EFTs are commonly used to interpret LHC data by integrating out heavy mediators. However, their validity breaks down when the energy scale of the collision approaches the mass of the heavy mediator ( $\Lambda$ ). Previous studies often relied on partonic center-of-mass energy ( $\sqrt{\hat{s}}$ ) to define validity, which is not directly observable.
The Gap: There is a lack of systematic comparison between EFT constraints and those derived from specific Ultraviolet (UV) complete models, particularly regarding how kinematic differences (like on-shell mediator production) affect exclusion limits and how automated simulation tools (like MadGraph5) handle scale choices differently for EFTs vs. UV models.
The Goal: To recast ATLAS monojet data to constrain a real scalar DM model ( $\phi$ ) using both a dimension-6 EFT ( $\phi$ SMEFT) and a specific UV completion (Vector-Like Quark Singlet model, VLQS), identifying regions where the two descriptions diverge and determining the complementarity with Direct Detection (DD) experiments.

2. Methodology

Theoretical Framework

The authors compare two frameworks for a real scalar DM candidate ( $\phi$ ) stabilized by a $Z_2$ symmetry:

$\phi$ SMEFT (EFT): A Standard Model Effective Field Theory extended with a real scalar singlet. The study focuses on dimension-6 operators coupling $\phi$ $ϕ$ to SM quarks and gluons:
- $O_{qdH\phi^2}$ and $O_{quH\phi^2}$ (quark operators).
- $O_{G\phi}$ (gluon operator).
VLQS (UV Completion): A specific model from Ref. [15] featuring two heavy vector-like quarks ( $Q \sim (3,2,1/6)$ $Q \sim (3, 2, 1/6)$ and $D \sim (3,1,-1/3)$ $D \sim (3, 1, - 1/3)$ ) and the scalar $\phi$ $ϕ$ . The VLQs decay into a jet and $\phi$ $ϕ$ (missing energy).
- Matching: The authors derive matching equations (Eq. 2.4) relating the Wilson Coefficients (WCs) of the EFT to the Yukawa couplings and masses of the VLQ model. Tree-level matching applies to quark operators, while gluon operators are generated at the 1-loop level.

Experimental Analysis

Data Source: Recast of the ATLAS monojet search using $140 \text{ fb}^{-1}$ of Run-II data.
Simulation:
- Tools: FeynRules for UFO model generation, MadGraph5_aMC@NLO for matrix elements, Pythia8 for parton showering, and Delphes3 for detector simulation.
- Strategy: The analysis uses exclusive $E_T$ bins (rather than inclusive) to better isolate the validity range of the EFT.
- Scale Choice: A critical methodological step involves the factorization/renormalization scale ( $\mu_{fac}$ ). The authors identify that the default dynamic scale in MadGraph5 causes mismatches between EFT and UV predictions. They switch to a fixed scale $\mu_{fac} = \sqrt{\hat{s}}$ to ensure consistent comparisons.
Statistical Approach: A $\chi^2$ fit is performed on the number of events in each $E_T$ bin, comparing the observed data (including background uncertainties) against the predicted BSM signal.

Complementary Constraints

Direct Detection (DD): Calculated spin-independent (SI) scattering cross-sections using nucleon form factors and compared against limits from PandaX-4T, LZ, DarkSide-50, and DEAP-3600.
Relic Density: Checked consistency with the Planck measurement ( $\Omega h^2 \approx 0.12$ ) using MadDM.

3. Key Contributions

Identification of EFT Validity Thresholds: The study demonstrates that the EFT description diverges from the UV completion at significantly lower energy scales than expected based on invariant mass alone.
- The $E_T$ distribution (observable) deviates from the UV model at $\sim 20\%$ of the new physics scale ( $\Lambda$ ), whereas the invariant mass $M(\phi\phi j)$ deviates at $\sim 70\%$ of $\Lambda$ .
The "On-Shell" Effect: The authors show that in the UV model, the production of on-shell vector-like quarks (mediators) creates a resonance peak in the cross-section near the mediator mass. This allows the UV model to accommodate large fluctuations in high- $E_T$ data bins (specifically the EM10 bin, $1000 < E_T < 1100$ GeV) with smaller couplings than the EFT, which lacks this resonant enhancement.
Simulation Scale Mismatch: A novel finding is that the default dynamic scale choice in MadGraph5 leads to a systematic mismatch in cross-section predictions between EFT and UV models. This discrepancy is resolved by using a fixed scale ( $\sqrt{\hat{s}}$ ), highlighting a potential pitfall in automated EFT vs. UV comparisons.
Complementarity of Monojet and DD: The paper maps out specific regions in parameter space where monojet constraints are superior to Direct Detection, particularly:
- For light DM masses ( $m_\phi \lesssim 2$ GeV) with gluon operators.
- For flavor-off-diagonal couplings (e.g., $d \to s$ transitions) which are not probed by DD.
- In scenarios where DD cross-sections are suppressed due to cancellations between different operator contributions (dependent on the target nucleus $Z/A$ ratio).

4. Key Results

EFT vs. UV Constraints:
- When using all $E_T$ bins, the EFT constraints appear much weaker than the UV constraints because the EFT cannot reproduce the resonant enhancement seen in the UV model at high energies.
- When restricting the analysis to low $E_T$ bins ( $< 350$ GeV), the EFT and UV constraints become nearly identical. However, in this low-energy regime, the constraints are often weaker than simple perturbative unitarity bounds, offering little new phenomenological insight.
- The apparent exclusion of the Standard Model (SM) point in the EFT analysis is traced to a large statistical fluctuation in the EM10 bin of the ATLAS data, which the UV model can accommodate via on-shell production but the EFT cannot.
LHC Reach:
- For the VLQS model with $M_Q = M_D = 3$ TeV, monojet searches constrain the Yukawa couplings to $|y| \lesssim 1.8$ (below the perturbativity limit of $\sqrt{4\pi} \approx 3.5$ ).
- Future HL-LHC projections ( $3000 \text{ fb}^{-1}$ ) suggest a sensitivity improvement of $\sim 32\%$ for EFT couplings and $\sim 68\%$ for VLQ couplings.
Direct Detection vs. Collider:
- Generally, DD experiments provide stronger constraints for quark-mediated operators.
- However, for the gluon operator ( $O_{G\phi}$ ), monojet searches are the strongest constraint for $m_\phi \lesssim 2$ GeV.
- Monojet searches uniquely constrain flavor-off-diagonal couplings (e.g., $C_{12}$ ) which are invisible to DD.

5. Significance

This paper provides a critical "reality check" for the use of EFTs in Dark Matter searches at colliders.

Methodological Rigor: It establishes that relying solely on partonic energy cuts is insufficient; observable proxies like $E_T$ must be used, and simulation scale choices must be carefully standardized when comparing EFTs to UV models.
Phenomenological Insight: It highlights that "safe" EFT regions (low $E_T$ ) often yield constraints no better than theoretical perturbativity limits, while "unsafe" regions (high $E_T$ ) where EFTs break down can be misleading if interpreted without a UV completion.
Strategic Value: The study underscores the necessity of combining collider and direct detection data. Specifically, it identifies "blind spots" in DD (flavor-off-diagonal couplings, specific mass ranges for gluon operators) where LHC monojet searches are the primary or only probe, ensuring a comprehensive coverage of the DM parameter space.

In conclusion, the authors demonstrate that while EFTs are useful tools, their application to LHC data requires careful validation against specific UV completions to avoid misinterpreting kinematic features (like resonances) and simulation artifacts (scale choices) as physical constraints.