Search for Invisibly Decaying Light Scalars at the FCC-ee

This paper investigates the potential discovery of invisibly decaying light scalars at the FCC-ee operating at 240 GeV by analyzing their production in association with hadronically decaying Z bosons, demonstrating that the collider could achieve sensitivities of 0.01–1 fb and potentially discover new scalars with masses up to 80 GeV depending on the mixing angle.

The Gist

Imagine the universe is a giant, high-speed particle collision game, like a cosmic pinball machine. For decades, physicists have been playing this game with the Standard Model, which is their rulebook. The rulebook works great, but it's missing a few pages. It can't explain things like "Dark Matter" (the invisible stuff holding galaxies together) or why there's more matter than antimatter in the universe.

This paper is a proposal for a new, super-advanced version of that pinball machine called the FCC-ee (Future Circular Collider). The authors are asking: "What if we smash particles together at a specific speed (240 GeV) and look for a very specific, sneaky new player?"

Here is the breakdown of their search, using simple analogies:

1. The "Invisible Ghost" and the "Heavy Bouncer"

The scientists are looking for a new, light particle called a scalar. Think of this particle as a "ghost."

• The Ghost: It's so light and sneaky that when it is created, it doesn't leave a trace in the detector. It just vanishes. This is what they mean by "invisibly decaying."
• The Bouncer: To catch this ghost, they need a partner. They propose creating the ghost alongside a Z boson (a heavy particle). Think of the Z boson as a loud, heavy bouncer. When the bouncer is created, it immediately breaks apart into two jets of regular particles (quarks) that the detectors can see.

The Strategy: If the bouncer (Z boson) appears and then suddenly vanishes into thin air (missing energy), it means the ghost (the new scalar) was there with it, stealing the energy.

2. The "Missing Money" Trick

How do you know the ghost is there if you can't see it? You use the Recoil Mass technique.
Imagine you are at a carnival game where you throw a ball (the collision energy) at a target.

• If you throw the ball and it hits a heavy object (the Z boson), you can measure how hard that object flies away.
• If the object flies away with less energy than you threw, you know something else must have been there to "steal" that energy.
• By measuring exactly how much energy is missing, the scientists can calculate the "weight" (mass) of the invisible ghost, even though they never saw it.

3. The "Needle in a Haystack" Problem

The problem is that the universe is messy. There are many other processes that look like a missing-energy event. It's like trying to find a specific needle in a haystack, but the haystack is made of other needles that look almost exactly the same.

• The Haystack: These are "background" events, like two Z bosons colliding or other standard particle interactions that happen naturally.
• The Needle: The new light scalar.

To find the needle, the authors used two strategies:

1. The Ruler Method (Selection): They set strict rules. "Only look at events where the missing energy is exactly this much, and the Z boson is flying at this angle." It's like saying, "Only look for needles that are exactly 3 inches long."
2. The AI Detective (MVA/BDT): They trained a computer program (a Boosted Decision Tree) to be a super-sleuth. They fed the computer millions of examples of "fake needles" (background) and "real needles" (signal). The computer learned to spot tiny, subtle differences in the patterns of the collision that a human ruler couldn't see. It's like teaching a dog to sniff out a specific scent in a crowded room.

4. What Did They Find? (The Results)

The authors ran simulations to see how well this plan would work if the FCC-ee were built.

• The Sweet Spot: They found that if the "ghost" particle is light (between 15 and 80 GeV), the detectors would be very good at finding it. The "AI Detective" could spot it clearly against the background noise.
• The Foggy Areas: If the ghost is heavier (around 80–120 GeV), it gets harder to find. This is because the "noise" from other standard particles (like the Z boson and the Higgs boson) gets louder and muddies the signal. It's like trying to hear a whisper in a room where a band is playing.
• The Goal: They calculated that with enough data (10.8 years of running), they could detect these particles if they exist, with a sensitivity that is incredibly precise (down to 0.01 "femtobarns," which is a tiny unit of probability).

5. The Bottom Line

This paper doesn't claim they found the ghost. Instead, it's a blueprint.

• It says: "If we build this machine and run it at this speed, here is exactly how we should look for these invisible particles."
• It confirms that if these light, invisible scalars exist, the FCC-ee has the tools to catch them, especially if they are lighter than the Z boson.
• It also provides a "rulebook" (a computer model) that other scientists can use to test their own theories against this specific search strategy.

In short, they are designing a highly sensitive metal detector for a beach, telling us exactly where to dig and what the metal sounds like, in case there are buried coins (new physics) hidden in the sand.

Technical Summary

Technical Summary: Search for Invisibly Decaying Light Scalars at the FCC-ee

Problem and Motivation
While the Standard Model (SM) successfully describes most particle physics measurements, it fails to explain phenomena such as the nature of dark matter and the matter-antimatter asymmetry. Extensions of the SM scalar sector, particularly those introducing additional light scalars, are a primary theoretical avenue to address these gaps. Although existing experimental constraints do not yet exclude low-mass scalar states, their detection requires high-luminosity colliders. This paper investigates the potential of the Future Circular Collider-ee (FCC-ee) operating at a center-of-mass energy of $\sqrt{s} = 240$ GeV to discover light scalars ($M_S \leq 120$ GeV) that decay invisibly. The study focuses on the production channel $e^+e^- \to Z S$, where the $Z$ boson decays hadronically ($Z \to q\bar{q}$) and the new scalar $S$ decays into invisible dark matter candidates.

Methodology
The analysis employs a simplified extension of the Standard Model incorporating a real scalar singlet and a dark matter candidate ($\chi$). The model includes a Higgs-singlet portal coupling and allows for mixing between the SM Higgs boson and the new scalar. The parameter space is scanned over scalar masses ($M_1$) ranging from 15 to 120 GeV, with fixed mixing angles ($\sin \alpha$) and dark matter mass ($M_\chi = 5$ GeV). Constraints on perturbativity and the invisible branching fraction of the SM Higgs ($<10\%$) are applied.

The simulation chain utilizes:

• Signal Generation: MadGraph5_aMC@NLO with a custom UFO model (DM_OHSM) to generate $e^+e^- \to Z\chi\chi$ events, including interference effects with the SM Higgs.
• Background Generation: Central FCC-ee Winter2023 campaign samples for processes including $ZZ$, $WW$, $Z/\gamma^* \to q\bar{q}$, and various Higgs-strahlung processes ($ZH$) with invisible decays.
• Detector Simulation: A parametric response of the IDEA detector implemented in Delphes, accounting for Initial State Radiation (ISR), Final State Radiation (FSR), and Gaussian beam spread.
• Analysis Strategy: Two complementary approaches are used:
  1. Selection-based: Cuts on jet kinematics, missing momentum ($p_{miss}$), and recoil mass ($M_{recoil}$).
  2. Multivariate Analysis (MVA): A Boosted Decision Tree (BDT) trained using XGBoost to discriminate signal from background based on kinematic variables (jet energies, angles, missing momentum, and recoil mass).

Key Contributions

• Model Implementation: Development and public release of a UFO model (DM_OHSM) for simulating singlet scalar production with invisible decays, including Higgs interference effects.
• Improved Background Modeling: Incorporation of ISR, FSR, and beam spread effects in the background simulation, extending previous analyses.
• Comprehensive Sensitivity Study: Evaluation of discovery potential and exclusion limits across the full mass range (15–120 GeV) for varying mixing angles, utilizing both cut-based and MVA techniques.

Results

• Significance: The expected Asimov significance ($Z$) is highest for scalar masses below the $Z$ boson mass ($M_Z$), where backgrounds are lower. A dip in sensitivity is observed near $M_Z$ due to the $ZZ \to q\bar{q}\nu\bar{\nu}$ background and near the SM Higgs mass ($125$ GeV) due to $ZH$ backgrounds. For mixing angles $\sin \alpha \leq 0.99$, scalars with masses up to 80 GeV are within discovery reach (significance $\geq 5\sigma$).
• Exclusion Limits: The study derives expected 95% Confidence Level (CL) upper limits on the production cross-section times the invisible branching fraction, $\sigma(e^+e^- \to q\bar{q}h_1) \times \mathcal{B}(h_1 \to \text{inv})$.
  • For $M_S < M_Z$, sensitivities of $\sim 10^{-2}–10^{-1}$ fb are achievable.
  • For the mass range 80–120 GeV, sensitivities of 0.1–1 fb are obtained.
• Mixing Angle Dependence: The derived limits are found to be largely independent of the mixing angle ($\sin \alpha$) within the tested range (0.973–0.995).
• Variable Importance: In the MVA analysis, missing momentum ($p_{miss}$) is identified as the dominant variable for discriminating signal from background, particularly for lower scalar masses.

Significance
The paper demonstrates that the FCC-ee, operating as a Higgs factory, possesses significant sensitivity to light scalars decaying invisibly in association with a hadronically decaying $Z$ boson. The study provides a concrete framework for projecting sensitivity onto specific Beyond the Standard Model (BSM) scenarios using the DM_OHSM model. By establishing that novel scalars up to 80 GeV are within discovery reach, the work supports the prioritization of such searches in the physics program for future lepton colliders. The results offer a baseline for experimental collaborations to project their specific model spaces and refine sensitivity estimates.