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Search for quantum black hole production in lepton+jet final states using proton-proton collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

Using 140 fb $^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the ATLAS detector, this study found no evidence of quantum black holes in lepton+jet final states, setting a lower mass threshold limit of 8.8 TeV in the Arkani-Hamed-Dimopoulos-Dvali model and 6.3 TeV in the Randall-Sundrum model.

Original authors: ATLAS Collaboration

Published 2026-08-25

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CC BY 4.0

Original authors: ATLAS Collaboration

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

The universe as we understand it is built on a foundation of particles and forces, a framework known as the Standard Model. This theory successfully explains how matter behaves and interacts, yet it leaves a profound mystery unsolved: why is gravity so incredibly weak compared to the other fundamental forces? While a magnet can lift a paperclip against the entire gravitational pull of the Earth, gravity remains the weakest of nature's forces by a staggering margin. To resolve this imbalance, some physicists have proposed that gravity might not be confined to the three dimensions of space we experience. Instead, it could be leaking into hidden, extra dimensions that are too small for us to see. If these extra dimensions exist, they would lower the energy scale required for gravity to become strong, potentially allowing it to manifest in ways we can detect.

In this scenario, if two particles collide with enough energy, they might not just bounce off each other; they could momentarily form a tiny, fleeting object known as a quantum black hole. Unlike the massive black holes found at the centers of galaxies, which are so heavy that they swallow everything nearby, these quantum versions would be microscopic and would vanish almost instantly. They would decay immediately into a spray of other particles. The question is whether we can catch a glimpse of these fleeting moments before they disappear. If we can find them, it would be direct proof that extra dimensions exist and that gravity behaves differently at the smallest scales than it does in our everyday world.

At the Large Hadron Collider, a massive particle accelerator buried underground near Geneva, scientists smash protons together at nearly the speed of light to recreate the extreme conditions of the early universe. The ATLAS detector, a colossal machine the size of a cathedral, records the debris from these collisions. In a recent study, the ATLAS collaboration used data corresponding to 140 inverse femtobarns of integrated luminosity to search for the specific signature of these quantum black holes. They were looking for a very particular event: a collision that produces a single high-energy electron or muon (a heavy cousin of the electron) paired with a jet of particles. In the models the researchers were testing, a quantum black hole would form and then decay into exactly this combination: one lepton and one quark, the latter appearing as a jet.

The team analyzed the data with a focus on the total energy, or invariant mass, of these electron-jet and muon-jet pairs. If a quantum black hole had been created, it would have appeared as a sudden spike in the number of events at a specific high mass, standing out clearly against the smooth, predictable background of ordinary particle interactions. The researchers looked for these spikes in a region where the mass was greater than 2.0 TeV, a threshold high enough to ensure they were looking for new physics rather than known processes. They examined the data with extreme care, accounting for every possible source of error and background noise, from the way the detector measures energy to the subtle effects of multiple collisions happening at once.

The result was a clear and consistent picture of the known universe. The distribution of the data points agreed with the predictions of the Standard Model within the expected uncertainties. There were no unexpected spikes, no sudden surges of events that could be attributed to the formation of a quantum black hole. The observed data looked exactly like what the scientists expected to see if only ordinary particles were interacting. This absence of a signal is, in itself, a significant discovery. It allows the researchers to set strict limits on how heavy these quantum black holes could possibly be. They determined that if these objects exist, they must be heavier than 8.8 TeV in the model with six extra dimensions, and heavier than 6.3 TeV in the model with one extra dimension.

These new limits represent a substantial improvement over previous searches. By pushing the boundary of what is possible to detect, the study effectively rules out the existence of quantum black holes in the lower mass ranges that were previously accessible. It tells us that if nature is hiding these extra dimensions and the associated quantum black holes, they are hiding at energies even higher than we have been able to reach so far. The search continues, but for now, the universe remains silent on the presence of these specific quantum objects in the energy range explored by the ATLAS detector. The Standard Model stands firm, and the quest to find the cracks in its foundation must move to even higher energies.

Technical Summary: Search for Quantum Black Hole Production in Lepton+Jet Final States at $\sqrt{s}=13$ TeV

Problem and Motivation
This paper addresses the search for Quantum Black Holes (QBHs), a prediction of low-scale quantum gravity models that propose solutions to the Standard Model (SM) mass hierarchy problem. These models lower the scale of quantum gravity ( $M_D$ ) from the Planck scale ( $\sim 10^{16}$ TeV) to the TeV region (1–10 TeV). The analysis focuses on two specific theoretical frameworks: the Arkani-Hamed-Dimopoulos-Dvali (ADD) model, which posits large extra dimensions ( $n=6$ in this analysis), and the Randall-Sundrum (RS1) model, which involves a single warped extra dimension ( $n=1$ ).

Unlike semiclassical black holes that decay via Hawking radiation into multiparticle final states, QBHs are postulated to decay into two-particle final states (specifically a lepton and a quark) while conserving total angular momentum, color, and electric charge, though potentially violating global symmetries like baryon or lepton number. The study targets the lepton+jet ( $e$ +jet and $\mu$ +jet) invariant mass spectra to identify such resonances.

Methodology
The analysis utilizes 140 fb $^{-1}$ of proton-proton collision data collected by the ATLAS detector at the Large Hadron Collider (LHC) at a center-of-mass energy of $\sqrt{s}=13$ TeV during the 2015–2018 run.

Event Selection: Candidate events are required to contain a leading lepton (electron or muon) and a leading jet, both with transverse momentum ( $p_T$ ) greater than 130 GeV. The invariant mass ( $m_{inv}$ ) of the lepton+jet pair must exceed 2.0 TeV. Subleading leptons with $p_T > 10$ GeV are vetoed, and subleading jets are required to have $p_T < 130$ GeV to suppress SM background.
Background Estimation: The dominant background is $W$ $W$ +jets, followed by contributions from $Z$ $Z$ +jets, top-quark pair ( $t\bar{t}$ $t \overset{ˉ}{t}$ ), single-top, diboson, and multijet processes.
- $W$ +jets, $Z$ +jets, and $t\bar{t}$ normalizations are constrained using dedicated Control Regions (CRs) orthogonal to the Signal Region (SR) and validated in Validation Regions (VRs).
- The multijet background in the electron channel is estimated using a data-driven Matrix Method.
- In the muon channel, the fake/non-prompt lepton background is negligible (<0.5% of total background).
Signal Modeling: QBH signal samples are generated using the QBH 3.0 generator, interfaced with Pythia 8 for parton showering and hadronization. The simulation assumes massless parton interactions and conserves total angular momentum. The threshold mass ( $M_{th}$ ) is set equal to $M_D$ .
Statistical Analysis: A profile likelihood fit is performed using the HistFitter framework. The analysis employs both model-independent fits (testing for any non-SM signal) and model-dependent fits (specifically for ADD and RS1 scenarios). Systematic uncertainties, including jet energy scale/resolution, lepton identification, and modeling uncertainties, are treated as nuisance parameters. A correction factor ( $R_c \approx 0.37$ ) is applied to account for higher-order QCD radiation effects, which otherwise distort the signal acceptance due to the veto on subleading jets.

Key Contributions and Results
The observed invariant mass spectrum of lepton+jet pairs is consistent with Standard Model expectations across the entire range, with no significant excess observed in either the electron+jet or muon+jet channels.

Upper Limits: 95% confidence level (C.L.) upper limits are set on the production cross-section times branching fraction ( $\sigma \times \mathcal{B}r$ ) for QBHs decaying into a lepton and a quark.
Mass Threshold Limits:
- In the ADD model ( $n=6$ ), the lower mass threshold limit is established at 8.8 TeV.
- In the RS1 model ( $n=1$ ), the lower mass threshold limit is established at 6.3 TeV.
Model-Independent Limits: For a non-SM signal with $m_{inv} > 5$ TeV, the upper limit on $\sigma \times \mathcal{B}r$ is 0.052 fb for the combined channel.

Significance
The paper claims that these results represent a significant improvement over previous searches. Specifically:

The limit on the QBH threshold mass for the ADD model is 3.5 TeV higher than the previous ATLAS result obtained at 8 TeV.
The obtained limits show a factor of 3.5 improvement with respect to the previous model-independent upper limit on $\sigma \times \mathcal{B}r$ .
This is the first time a limit on the QBH threshold mass for the RS1 model has been determined in the lepton+jet decay mode.

The analysis demonstrates that the lepton+jet channel, while generally less sensitive than dijet searches, provides complementary constraints on QBH production with different quantum numbers and can effectively constrain models violating baryon-lepton global symmetries. The results place stringent constraints on low-scale quantum gravity scenarios within the tested mass ranges.

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