Search for quantum black holes in lepton+jet final states using proton-proton collisions at $\sqrt{s}=13.6$ TeV with the ATLAS detector

Using 164 fb⁻¹ of proton-proton collision data at 13.6 TeV collected by the ATLAS detector during Run 3, this study reports no significant excess of quantum black hole candidates in lepton+jet final states and establishes the world's strongest exclusion limits to date, reaching a mass scale of 9.4 TeV.

The Gist

The Cosmic "Smash-and-Grab": Hunting for Tiny Black Holes at CERN

Imagine the Large Hadron Collider (LHC) as the world's most powerful cosmic pinball machine. It shoots tiny particles (protons) at each other at nearly the speed of light, smashing them together to recreate the conditions of the universe just a fraction of a second after the Big Bang.

In this new paper, the ATLAS collaboration (a team of thousands of scientists) is playing a very specific game of "Where's Waldo?" They are looking for something incredibly exotic: Quantum Black Holes (QBHs).

Here is the breakdown of their mission, explained simply:

1. The Big Problem: Why Gravity is Weird

Scientists have two rulebooks for how the universe works:

• The Small Stuff: Quantum mechanics (atoms, particles).
• The Big Stuff: General relativity (gravity, planets, stars).

The problem is that these two rulebooks don't get along. Gravity is mysteriously weak compared to the other forces. Why is a tiny magnet strong enough to lift a paperclip against the gravity of the entire Earth?

The Theory: Some physicists think gravity isn't actually weak; it's just leaking out into extra dimensions we can't see. Imagine a spiderweb (our 3D world) where the spider (gravity) is actually huge, but its legs are stretching out into a 4th or 5th dimension. If we could get close enough, gravity would suddenly become super strong.

2. The Goal: Making a Tiny Black Hole

If these extra dimensions exist, smashing two protons together hard enough should create a Quantum Black Hole.

• Normal Black Holes: Think of a black hole like a giant, hungry vacuum cleaner in space. It eats everything nearby and spits out heat slowly over billions of years.
• Quantum Black Holes: These are the "micro" version. They are so small they don't have time to be "hungry." Instead of slowly eating, they instantly explode into a shower of particles.

The ATLAS team is looking for a very specific explosion: a Lepton + Jet.

• The Lepton: A high-energy electron or muon (a heavy cousin of the electron).
• The Jet: A spray of particles created from a quark (the building block of protons).

If they see a massive explosion of just these two things, it's a smoking gun for a Quantum Black Hole.

3. The Upgrade: Why Now?

The LHC recently got a power-up. It used to run at 13 TeV (Tera-electronvolts, a unit of energy). Now, it runs at 13.6 TeV.

The Analogy: Imagine you are trying to break a specific, very tough nut.

• At 13 TeV, you hit it with a hammer. It might crack, but it's hard.
• At 13.6 TeV, you hit it with a slightly heavier hammer.
• The Catch: Because of how the math of extra dimensions works, that tiny 0.6 TeV increase doesn't just make the hit 5% harder. It makes the chance of breaking the nut 100% to 1000% higher for the heaviest black holes.

It's like finding out that a slightly higher temperature doesn't just melt ice a little faster; it turns the whole block of ice into a puddle instantly. This small energy bump gave the scientists a massive boost in their chances of finding these black holes.

4. The Search: Looking for the "Ghost"

The team analyzed 164 "femtobarns" of data (a unit of collision data) collected between 2022 and 2024. That's a lot of data!

They looked at the "invariant mass" of the electron/muon and the jet.

• The Background Noise: Most of the time, when protons smash, they create messy debris (like a car crash). This is the "noise."
• The Signal: If a Quantum Black Hole exists, it would create a very specific, clean, high-energy pair (Lepton + Jet) that stands out against the noise.

The Result: They found nothing.
No Quantum Black Holes were spotted. The data looked exactly like what the Standard Model (our current best theory of physics) predicted.

5. The Silver Lining: Setting the "No-Go" Zone

Just because they didn't find the black holes doesn't mean the experiment failed. In science, ruling things out is just as important as finding them.

Think of it like searching for a lost key in a dark room.

• If you find the key, you are happy.
• If you don't find it, but you have a very bright flashlight and you checked every single corner, you can confidently say: "The key is not in this room."

The ATLAS team used their powerful "flashlight" (the 13.6 TeV energy) to say:

• "If Quantum Black Holes exist, they must be heavier than 9.4 TeV."
• This is the heaviest limit ever set for these particles. They have pushed the "No-Go" zone further than ever before.

Summary

• What they did: Smashed protons together at record energy levels to see if they could create tiny, exploding black holes.
• What they found: Nothing. The universe didn't give up its secret this time.
• Why it matters: They proved that if these black holes exist, they are even heavier and harder to find than we thought. This forces physicists to rethink their theories or wait for even more powerful machines in the future.

The hunt continues, but for now, the universe is keeping its extra dimensions and quantum black holes hidden!

Technical Summary

1. Problem and Motivation

The search addresses the hierarchy problem, the vast discrepancy between the electroweak scale ($\sim 10^2$ GeV) and the Planck scale ($\sim 10^{19}$ GeV). Theories involving Extra Dimensions (EDs), specifically the Arkani-Hamed, Dimopoulos, and Dvali (ADD) model and the Randall–Sundrum (RS) model, propose that gravity propagates into extra dimensions, lowering the fundamental gravity scale ($M_D$) to the TeV range.

If $M_D$ is low enough, proton-proton collisions at the Large Hadron Collider (LHC) could produce Quantum Black Holes (QBHs). Unlike semi-classical black holes that decay thermally via Hawking radiation into high-multiplicity states, QBHs are postulated to decay immediately into two-particle final states. This analysis specifically targets QBHs decaying into lepton + jet ($\ell + \bar{q}$) final states.

A critical motivation for this specific analysis is the strong dependence of the QBH production cross-section ($\sigma_{QBH}$) on the center-of-mass energy ($\sqrt{s}$). The transition from Run 2 ($\sqrt{s}=13$ TeV) to Run 3 ($\sqrt{s}=13.6$ TeV) results in a dramatic increase in $\sigma_{QBH}$ (up to 1000% for masses around 10.5 TeV) due to the reduced suppression of parton distribution functions (PDFs) at high Bjorken-$x$. This allows for significantly improved exclusion limits even with a dataset size comparable to Run 2.

2. Methodology

Data and Simulation

• Dataset: The analysis uses $164 \text{ fb}^{-1}$ of proton-proton collision data recorded by the ATLAS detector at $\sqrt{s}=13.6$ TeV during the 2022–2024 Run 3 period.
• Signal Models: QBHs are simulated using the QBH v3.02 generator.
  • ADD Model: Assumes $n=2, 4, 6$ extra dimensions.
  • RS Model: Assumes $n=1$ warped extra dimension.
  • Threshold Mass ($M_{th}$): Ranges from 6 to 10.5 TeV. The analysis focuses on the mass region $(1-3)M_{th}$ where quantum effects dominate.
• Backgrounds: Dominant backgrounds include $W$+jets, $Z$+jets, $VV$ (diboson), and top-quark processes ($t\bar{t}$, single-top). These are modeled using Monte Carlo (MC) simulations (Sherpa, Powheg, MadGraph).
• Fakes: Non-prompt electrons (from photon conversions or jets misidentified as electrons) are estimated using a Matrix Method (MM) based on data-driven techniques.

Event Selection

The search targets electron+jet and muon+jet final states with high invariant mass ($m_{\ell j}$).

• Lepton Selection:
  • Electrons: $p_T > 150$ GeV, $|\eta| < 2.47$ (excluding transition regions), Tight identification, and High-$p_T$ isolation.
  • Muons: $p_T > 150$ GeV, $|\eta| < 2.5$, High-$p_T$ identification, and PflowTightVarRad isolation.
• Jet Selection: Reconstructed with the anti-$k_t$ algorithm ($R=0.4$), $p_T > 130$ GeV, $|\eta| < 2.5$.
• Signal Region (SR) Cuts:
  • Exactly one signal lepton and at least one signal jet.
  • Invariant mass $m_{\ell j} > 3$ TeV.
  • Angular separation: $\Delta\phi_{\ell j} > 2.8$ and $\Delta\eta_{\ell j} < 3.25$ (exploiting the back-to-back topology of QBH decay).
  • Missing transverse momentum significance $S(p_T^{miss})$ is used to distinguish signal from backgrounds.

Background Estimation

• $W$+jets and $Z$+jets: Normalization factors are derived from Control Regions (CRs) defined in lower mass ranges ($1.0-2.0$ TeV) and validated in Validation Regions (VRs).
• Fake Electrons: Estimated via the Matrix Method in a dedicated "fake-enriched" CR ($f$CR) and validated in a "fake VR" ($f$VR).
• Fit Procedure: A simultaneous profile-likelihood fit is performed across the Signal Region, $W$CR, and $Z$CR to constrain background normalizations and systematic uncertainties.

Systematic Uncertainties

Key uncertainties include:

• Theoretical: QCD scale variations and PDF uncertainties for $W/Z$+jets ($\sim 30\%$).
• Experimental: Lepton/jet energy scales, resolution, identification efficiencies, and luminosity ($\sim 1.8\%$).
• Fakes: Uncertainty in the origin of fake electrons (light-flavor decays vs. photon conversions) and statistical limitations in the $f$CR.

3. Key Contributions

• First Run 3 Results: This is the first ATLAS search for QBHs utilizing the full Run 3 dataset at 13.6 TeV.
• Energy Sensitivity: It explicitly demonstrates the power of the 0.6 TeV energy increase from Run 2 to Run 3, which enhances the QBH production cross-section by orders of magnitude at high masses.
• Channel Separation: The analysis treats electron and muon channels separately, noting that the electron channel offers superior sensitivity due to better momentum resolution and lower background levels.
• Data-Driven Backgrounds: Robust application of the Matrix Method for fake electron estimation in the high-mass regime.

4. Results

• Observation: No significant excess of events was observed above the Standard Model (SM) background in either the electron or muon channels.
• Highest Mass Events:
  • Electron Channel: Highest observed event at $m_{\ell j} = 5.3$ TeV.
  • Muon Channel: Highest observed event at $m_{\ell j} = 5.5$ TeV.
  • Both events are consistent with SM background expectations.
• Exclusion Limits (95% CL):
  • RS Model ($n=1$): Excluded for threshold masses $M_{th} < 7.2$ TeV.
  • ADD Model ($n=6$): Excluded for threshold masses up to 9.4 TeV (electron channel) and 9.0 TeV (muon channel).
  • The electron channel provides limits roughly 3 times more sensitive than the muon channel due to superior mass resolution (electron+jet resolution < 5% vs. muon+jet 25–30%).
• Comparison: These limits represent the world's strongest exclusion limits to date for quantum black hole production in lepton+jet final states, surpassing previous Run 2 results despite a similar integrated luminosity, solely due to the energy gain.

5. Significance

This paper establishes the current frontier in the search for extra dimensions and quantum gravity signatures at the LHC.

1. Validation of Energy Scaling: It confirms theoretical predictions that a modest increase in collision energy (13 TeV $\to$ 13.6 TeV) yields a massive gain in sensitivity for high-mass BSM physics, validating the strategy of Run 3.
2. Stringent Constraints: By excluding QBH production up to 9.4 TeV, the analysis severely constrains the parameter space for ADD and RS models, pushing the lower bound of the fundamental gravity scale ($M_D$) higher than ever before.
3. Methodological Benchmark: The analysis sets a standard for handling high-mass resonances and data-driven background estimation in the high-luminosity era of the LHC.

In conclusion, while no evidence for quantum black holes was found, the analysis significantly narrows the search space for new physics, demonstrating the ATLAS detector's capability to probe energy scales approaching the Planck scale in the context of extra-dimensional theories.