Missing-mass search in forward-proton-tagged dilepton… — Plain-Language Explanation

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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

The Big Idea: Catching the Invisible by Watching the Outgoing

Imagine you are at a busy train station. Two trains (protons) zoom past each other on parallel tracks without crashing. However, as they pass, they exchange a few "high-fives" (photons). These high-fives are so energetic that they create a brand new, tiny particle right in the middle of the station.

Usually, when scientists look for new particles, they wait for the trains to crash head-on, creating a massive explosion of debris that they can sift through. But here, the trains don't crash; they stay intact and keep rolling. The only thing that changes is that they lose a tiny bit of speed because they gave away some energy to create that new particle in the middle.

The Goal: The ATLAS team at CERN is trying to find a "Ghost Particle" (called X) that is invisible to their detectors. They suspect this ghost might be related to Dark Matter, the mysterious stuff that holds the universe together but we can't see.

The Detective Work: The "Missing Mass" Trick

How do you find something you can't see? You use a trick called Missing Mass.

Think of it like a bank robbery where the thieves leave no fingerprints, but the security cameras catch the getaway drivers.

The Drivers (Forward Protons): The two proton trains keep moving forward but slow down slightly. The ATLAS detector has special sensors (the AFP spectrometer) located far down the track to catch these slowing drivers and measure exactly how much speed they lost.
The Loot (The Visible Part): In the center of the station, the energy from the "high-fives" creates a visible particle (a Z boson) that immediately splits into two charged particles (electrons or muons). The main detector sees these two clearly.
The Ghost (The Invisible Part): The energy balance equation is simple:
- Total Energy Given = Energy of Visible Loot + Energy of the Ghost.
- Since the scientists know exactly how much energy the drivers lost (Step 1) and exactly how much energy the visible loot has (Step 2), they can do the math to find the weight of the Ghost.

If the math shows a specific weight that doesn't match any known particle, they might have found something new!

The Challenge: The "Crowded Station" Problem

The biggest problem in this experiment is noise. The LHC is like a super-busy train station where thousands of trains pass by every second.

Sometimes, a proton from one collision slows down, and a pair of electrons from a completely different collision happens to fly by at the same time.
The computer might get confused and think, "Oh, these two slow protons and these two electrons came from the same event!" This creates a fake signal (background noise).

The Solution: The "Silence" Rule (Track Veto)
To fix this, the scientists added a strict rule: "If you see any other footprints (tracks) near the main event, throw the whole event out."

Real "Ghost" events are very clean. The protons don't crash, so they don't create a shower of debris. Only the two specific particles (the loot) should be there.
Fake events (from collisions) usually have a messy background with extra tracks.
By demanding a "clean room" with no extra footprints, the team successfully filtered out 99% of the noise, making their search much more sensitive than previous attempts.

The Search: What Did They Look For?

They scanned a wide range of "weights" (masses) for the Ghost particle, from 100 GeV to 900 GeV. They tested three different theories (models) of what this ghost might be:

The Generic Ghost: A standard invisible particle created alongside a Z boson.
The Axion Twin: A scenario involving two "Axion-Like Particles" (hypothetical dark matter candidates), where one is visible and the other is the invisible ghost.
The Loop Ghost: A more complex quantum process where the particles interact in a loop before creating the ghost.

The Results: No Ghosts Found (Yet)

After analyzing data from 2017 (equivalent to 14.7 "inverse femtobarns" of collisions—a fancy way of saying a huge amount of data), the result was:

No significant excess: They didn't find a spike in the data that indicated a new particle. The "Ghost" wasn't there, or at least not in the weight range they checked.
Setting Limits: Even though they didn't find it, they set very strict rules. They can now say, "If this Ghost particle exists, it cannot be heavier than X or lighter than Y, and it cannot be created more often than Z times."

Why This Matters

Even though they didn't find the "Holy Grail" particle, this paper is a huge success for two reasons:

Better Tools: They proved that using the "Missing Mass" technique combined with the "Silence Rule" (track veto) works incredibly well. It allowed them to see much further into the low-mass range than previous experiments (like the one at the CMS detector).
Ruling Out Possibilities: In science, knowing what isn't there is just as important as knowing what is. By ruling out these specific models, they force theorists to come up with new, smarter ideas about what Dark Matter might actually be.

In a nutshell: The ATLAS team acted like ultra-precise accountants. They watched two protons lose a tiny bit of energy, saw what they did create, and calculated exactly what they didn't see. They found no evidence of a new invisible particle, but they tightened the noose around where that particle could possibly hide.

1. Problem and Motivation

The Standard Model (SM) of particle physics cannot explain phenomena such as dark matter (DM), the hierarchy of particle masses, or matter-antimatter asymmetry. While many searches for Beyond the Standard Model (BSM) physics target specific theoretical models, they are often restricted to narrow phase spaces.

This paper addresses the need for model-independent searches capable of detecting invisible particles produced in association with visible systems. Specifically, it investigates the process of exclusive photon-photon fusion ( $pp \to p(\gamma\gamma \to V X)p$ ), where:

Two protons interact by exchanging photons.
The protons remain intact but lose a fraction of their energy, becoming deflected from the beam.
A visible boson ( $V$ ) is produced, decaying into a pair of same-flavor charged leptons ( $e^+e^-$ or $\mu^+\mu^-$ ).
An invisible system ( $X$ ), potentially a BSM particle or DM candidate, is produced alongside $V$ .

The challenge lies in reconstructing the properties of the invisible system $X$ without prior knowledge of its mass or decay modes.

2. Methodology

Data and Detector

Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the ATLAS detector in 2017, corresponding to an integrated luminosity of 14.7 fb $^{-1}$ .
Forward Proton Spectrometer (AFP): The analysis utilizes the ATLAS Forward Proton (AFP) spectrometer, located $\pm 205$ m and $\pm 217$ m from the interaction point. It detects intact protons that have lost energy but remain in the beam pipe.
Central Detector: The inner detector, calorimeters, and muon spectrometer measure the central dilepton system.

The Missing-Mass Method

The core technique relies on kinematic reconstruction:

Proton Measurement: The fractional energy loss ( $\xi$ ) of the forward protons is measured by the AFP. This allows the reconstruction of the four-momentum of the initial photon-photon system ( $P_{\gamma\gamma}$ ).
Central Measurement: The four-momentum of the visible dilepton system ( $P_V$ ) is measured in the central detector.
Inference: The four-momentum of the invisible system ( $P_X$ ) is inferred by subtraction: $P_X = P_{\gamma\gamma} - P_V$ .
Missing Mass ( $m_X$ ): The invariant mass of the invisible system is calculated as:
$m_X^2 = (E_{\gamma\gamma} - E_V)^2 - (\vec{p}_{\gamma\gamma} - \vec{p}_V)^2$
This allows the reconstruction of $m_X$ without knowing the properties of $X$ .

Event Selection and Background Suppression

Trigger: Single-lepton or dilepton triggers with low $p_T$ thresholds.
Proton Requirement: Exactly one "tight" proton ( $0.035 < \xi < 0.08$ ) detected on each side of the AFP spectrometer.
Lepton Selection: High-quality electrons or muons with $p_T > 18/15$ GeV and $m_{\ell\ell} > 50$ GeV.
Track Veto (Key Innovation): A strict requirement that no additional tracks with $p_T > 500$ MeV are associated with the dilepton vertex within a $z$ -distance of 0.5 mm. This significantly suppresses combinatorial backgrounds (e.g., $Z$ +jets) where additional hadronic activity is present, a feature not utilized in previous similar CMS analyses.

Background Modeling

Combinatorial Background: The dominant background arises from the coincidence of a central dilepton (from SM processes like $Z$ +jets, $t\bar{t}$ ) and uncorrelated pile-up protons.
Data-Driven Approach: An event-mixing technique is used. Central detector information from one event is combined with proton information from a different event to model the uncorrelated background. This avoids reliance on Monte Carlo (MC) modeling of the underlying event, which is known to be imprecise for track-veto efficiency.
Validation: The data-driven model was validated against MC simulations, showing good agreement.

3. Signal Models

Three simplified signal models were simulated to test sensitivity across different kinematic regimes:

$Z + H'$ Model: A generic scalar $H'$ (emulating an invisible particle) produced with a $Z$ boson via loop-induced interactions (simulated with MadGraph).
Di-ALP Model: Production of two Axion-Like Particles (ALPs), where one ( $S_1$ ) decays to leptons and the other ( $S_2$ ) is invisible (simulated with MadGraph).
$Z + X$ Model: A $Z$ boson produced with an invisible particle $X$ via a direct four-point interaction (simulated with SuperChic).

4. Key Results

Observation

No Significant Excess: The observed missing-mass spectrum ( $m_X$ ) in the range 100 GeV to 900 GeV is consistent with the Standard Model expectation. No narrow resonance was observed.

Limits on Fiducial Cross-Sections

Upper limits at 95% Confidence Level (CL) were set on the fiducial cross-sections for the three signal models:

Limits range between 128 fb and 2.5 fb, depending on the signal mass and model.
The most stringent limits (down to 2.5 fb) were achieved for the $Z+H'$ and Di-ALP models in the mass range of 600–800 GeV.

Model-Independent Limits

Model-independent upper limits on the visible cross-section ( $\sigma_{vis}$ ) for generic BSM processes were set.
With the track veto applied, limits reach the order of 1 fb in the 100–900 GeV mass range.
Without the track veto, limits are less stringent but cover a broader range of processes.

Comparison with CMS

For the common $Z+X$ model (SuperChic), this analysis shows a significant improvement in sensitivity over the previous CMS analysis for masses between 600 and 800 GeV.
Improvements of 770%, 160%, and 90% were observed for $m_X = 600, 700,$ and $800$ GeV, respectively.
Reason for Improvement: The primary driver is the track veto, which drastically reduces the dominant $Z$ +jets background, compensating for the fact that this analysis used less data (14.7 fb $^{-1}$ ) than the CMS analysis.

5. Significance and Conclusion

First of its Kind: This is the first ATLAS analysis to combine AFP forward proton data with the missing-mass method and the first to apply a central-track veto in this specific context.
Model Independence: The ability to reconstruct $m_X$ without assuming the properties of the invisible particle makes this a powerful tool for generic BSM searches, including Dark Matter candidates.
Technique Validation: The successful application of the event-mixing background model and the track veto demonstrates a robust methodology for future exclusive physics analyses at the LHC.
Complementarity: While the CMS PPS spectrometer has a higher $\xi$ acceptance (probing higher masses up to 1600 GeV), the ATLAS AFP analysis provides superior sensitivity in the lower mass region (100–900 GeV) due to the background suppression techniques employed.

In summary, the paper establishes a highly sensitive, model-independent search for invisible particles in exclusive photon-fusion events, setting stringent limits on BSM physics and demonstrating the power of forward proton tagging combined with central detector exclusivity requirements.

Missing-mass search in forward-proton-tagged dilepton events with the ATLAS detector