Prospects for Measuring $H\to \rm{invisble}$ at the FCCee

This paper presents a study demonstrating that the Future Circular Collider electron-positron (FCCee) operating at $\sqrt{s} = 240 \text{ GeV}$ with an integrated luminosity of 10.8 ab$^{-1}$ could achieve a 95% confidence level upper limit of 0.15% on the branching ratio of invisible Higgs decays by analyzing the $ZH$ production mode with $Z$ boson decays into electron-positron, muon-antimuon, and hadronic jets.

The Gist

Imagine the universe is a giant, high-speed dance floor where particles collide and create new, fleeting partners. One of the most famous dancers is the Higgs boson. Usually, when the Higgs boson is created, it quickly splits apart into other particles that our detectors can see, like flashes of light or tracks on a screen.

But sometimes, the Higgs boson might do something mysterious: it could decay into "invisible" particles (like ghosts) that pass right through our detectors without leaving a trace. The paper you provided is a proposal for how to catch these "ghosts" at a future super-collider called the FCC-ee.

Here is a simple breakdown of their plan:

1. The Setup: A Controlled Explosion

The scientists are planning to use a machine that smashes electrons and positrons (anti-electrons) together at a very specific speed (energy).

• The Goal: They want to create a specific event: a Z boson (a well-behaved, visible particle) paired with a Higgs boson.
• The Trick: Since the Higgs might disappear into invisibility, they can't look at the Higgs directly. Instead, they look at the Z boson. If they see a Z boson flying off in one direction, but the total energy and momentum of the collision don't add up, they know something is missing. That "missing" piece is the invisible Higgs.

2. The Three Ways to Watch the Z Boson

The Z boson is the "witness" to the crime. It can decay (break down) in three different ways, and the team analyzed all three:

• The Lepton Twins (Electrons or Muons): The Z boson splits into two charged particles (like electrons or muons). This is like seeing two bright spotlights. It's clean and easy to spot, but it happens rarely.
• The Jet Stream (Quarks): The Z boson splits into a spray of particles called "jets." This is like seeing a firework explode into a cloud of sparks. It happens much more often (about 20 times more often than the spotlights), but it's messier and harder to distinguish from background noise.

3. The Detective Work: Filtering the Noise

The collider will produce billions of collisions. Most of them are just "background noise"—ordinary events that look like the signal but aren't.

• The Filter: The researchers used a computer program (a "Boosted Decision Tree," which is like a super-smart digital detective) to sort through the data.
• The Criteria: They taught the computer to look for specific clues:
  • Did the Z boson have the right mass?
  • Is there a specific amount of "missing energy" (the ghost Higgs)?
  • Are the angles and speeds of the visible particles consistent with a Higgs disappearing?

4. The Results: Who Wins the Detective Game?

After running their simulations with the massive amount of data the FCC-ee is expected to collect, they found:

• The Lepton Channels (Electrons/Muons): These were very clean but too rare. The "detective" could only find a tiny hint of the invisible Higgs here, with a statistical significance of less than 1 sigma (basically, not enough to be sure it's real).
• The Jet Channel (Quarks): Even though this channel was messy, the sheer number of events allowed the detective to find a much stronger signal. They achieved a significance of 3.1 sigma. While this isn't a "discovery" yet (which requires 5 sigma), it is a strong hint.

5. The Final Verdict

The team combined all three channels to get the best possible answer.

• The Limit: They calculated that if the Higgs boson decays invisibly, it happens less than 0.15% of the time.
• What this means: If the Higgs decays invisibly more often than 0.15%, this experiment would have seen it. Since they didn't see a clear signal, they have set a very strict "speed limit" on how often this ghostly decay can happen.

Summary Analogy

Imagine you are trying to find out if a magician is making coins disappear.

• You set up a camera that records every time a coin is tossed.
• Sometimes the coin lands on the floor (visible decay).
• Sometimes the coin vanishes into thin air (invisible decay).
• The paper says: "We simulated watching 2.2 million coin tosses. We found that if the magician makes the coin vanish more than 15 times out of 10,000, we would have definitely noticed. Since we didn't see a clear pattern of vanishing coins, we can say the magician is very good at keeping the rate of vanishing coins below 0.15%."

This study doesn't claim to have found the invisible Higgs yet; it claims that with the Future Circular Collider, we will be able to prove that the invisible decay happens less than 0.15% of the time, or potentially discover it if it happens more often than that.

Technical Summary

Technical Summary: Prospects for Measuring H → Invisible at the FCC-ee

Problem and Motivation
In the Standard Model (SM), the Higgs boson possesses a small but non-zero branching fraction for invisible decays, primarily via $H \to ZZ \to \nu\bar{\nu}\nu\bar{\nu}$, estimated at 0.106%. While current LHC experiments (ATLAS and CMS) have established upper limits on this branching fraction, the Future Circular Collider electron-positron (FCC-ee) offers a unique environment for precision measurements. Operating at a center-of-mass energy of $\sqrt{s} = 240$ GeV with an integrated luminosity of 10.8 ab$^{-1}$, the FCC-ee is expected to produce approximately $2.2 \times 10^6$ Higgs bosons. This high yield, combined with the clean $e^+e^- \to ZH$ production mode, provides an opportunity to probe invisible Higgs decays with significantly improved sensitivity compared to hadron colliders. This study investigates the prospects for measuring the branching fraction $B(H \to \text{invisible})$ at the FCC-ee.

Methodology
The analysis focuses on the $ZH$ production process where the Higgs boson decays invisibly ($H \to \text{inv}$) and the $Z$ boson decays into three distinct channels:

1. Leptonic: $Z \to e^+e^-$
2. Leptonic: $Z \to \mu^+\mu^-$
3. Hadronic: $Z \to jj$ (including $b\bar{b}, c\bar{c}, s\bar{s}, q\bar{q}$)

Simulation and Event Generation:
Signal and background events were generated using Monte Carlo samples from the FCC-ee Winter2023 Campaign. The signal process $e^+e^- \to ZH$ with $H \to ZZ \to \nu\bar{\nu}\nu\bar{\nu}$ was simulated. Backgrounds included processes mimicking the signal, such as $ZZ$, $WW$, $Z\gamma^*$, and non-invisible Higgs production ($H \to ZZ, WW$). Event generation utilized Whizard3 and Pythia8, followed by parton showering and hadronization in Pythia6. Detector effects were modeled using the parametric response of the proposed IDEA detector via the Delphes software framework, incorporating initial and final state radiation and Gaussian beam spread.

Reconstruction and Selection:
The analysis was performed within the FCCAnalyses software framework. Events were categorized into three orthogonal channels based on the $Z$ decay products.

• Preselection: Required exactly two electrons or muons (for leptonic channels) or two jets (for hadronic channels) with $p > 5$ GeV, zero contamination from the other species, and a missing transverse momentum $p_{miss} > 5$ GeV. For the hadronic channel, jet clustering was performed using the exclusive Durham $k_T$ algorithm with $N_{jet}=2$.
• Kinematic Cuts: The $Z$ boson mass was constrained to $[87, 95]$ GeV. The recoil mass ($M_{Recoil}$), calculated from the visible $Z$ decay products, was required to be between 120 and 130 GeV to select Higgs candidates. A cut on the missing momentum angle, $|\cos \theta_{miss}| < 0.95$, was applied to suppress backgrounds.
• Multivariate Analysis (MVA): A Boosted Decision Tree (BDT) implemented in XGBoost was employed to further discriminate signal from background. Input features included kinematic observables (four-momenta, missing transverse momentum, visible energy, recoil mass) and derived variables such as momentum imbalance and ratios of transverse momenta. The BDT was trained on preselected events, and a final cut of MVA score $> 0.95$ was applied.

Key Results
The study evaluated the statistical significance and derived upper limits for the branching fraction $B(H \to \text{inv})$ in each channel and in combination:

• Significance: After the final MVA selection, the individual channels yielded low significances: $0.59\sigma$ for $Z(ee)$, $0.65\sigma$ for $Z(\mu\mu)$, and $3.14\sigma$ for $Z(jj)$. The higher sensitivity in the hadronic channel is attributed to the larger branching fraction of $Z \to \text{hadronic}$ ($\sim 69\%$) compared to leptonic decays ($\sim 3.4\%$), despite the higher background levels.
• Upper Limits: Using the CMS Combine software with the AsymptoticLimits function, 95% Confidence Level (CL) upper limits were calculated. The individual limits were:
  • $Z(ee)$: 0.43%
  • $Z(\mu\mu)$: 0.35%
  • $Z(jj)$: 0.15%
• Combined Limit: The combined upper limit on $B(H \to \text{invisible})$ across all three channels is 0.15%.

Significance and Claims
The paper claims that with the projected dataset of the FCC-ee at $\sqrt{s} = 240$ GeV, the experiment can set a stringent upper limit of 0.15% on the invisible Higgs branching fraction at 95% CL. This result represents a significant improvement over current limits and demonstrates the potential of the FCC-ee to precisely measure Higgs properties, even in the absence of a 5$\sigma$ discovery signal in the individual channels. The analysis highlights the critical role of the hadronic $Z$ decay channel in achieving the best sensitivity due to its higher event yield, validating the strategy of combining multiple decay modes to maximize the discovery potential for invisible decays.