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arxiv: 2604.10732 · v1 · submitted 2026-04-12 · ✦ hep-ex

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A search for microscopic black holes, string balls, and sphalerons in proton-proton collisions at sqrt{s} = 13 TeV

CMS Collaboration
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:25 UTC · model grok-4.3

classification ✦ hep-ex
keywords microscopic black holesstring ballselectroweak sphaleronslarge extra dimensionsCMS experimentLHC13 TeV collisionsbeyond standard model searches
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The pith

No signals for microscopic black holes, string balls or sphalerons appear in 13 TeV LHC data, excluding masses below 8.4-11.4 TeV in extra-dimension models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The CMS experiment searched a dataset of proton-proton collisions at 13 TeV equivalent to 138 inverse femtobarns for events that could indicate tiny black holes, string balls, or electroweak sphalerons. Two strategies relying on data-driven control samples found no excess over standard model expectations in final states with many energetic jets, leptons, and photons. This absence sets model-dependent limits that rule out black hole and string ball production in large extra dimension scenarios up to masses around 10 TeV. The same data also constrain the rate of sphaleron transitions above 9 TeV to a very small fraction of quark interactions. The results push the testable range for these exotic predictions to higher energies than earlier searches.

Core claim

In models with large extra dimensions, semiclassical black holes and string balls with masses below 8.4-11.4 TeV and 9.0-10.7 TeV respectively are excluded at 95% confidence level, while an upper limit of 0.0034 at 95% CL is set on the fraction of quark-quark interactions above the 9 TeV sphaleron threshold, based on the absence of signals in the full 138 fb^{-1} dataset analyzed with a new phase-space proximity classification method.

What carries the argument

Phase-space proximity classification that groups events by kinematic similarity to isolate candidates with multiple high-momentum jets, leptons, and photons from background using shape-invariant control samples.

If this is right

  • Semiclassical black hole production cannot occur at LHC energies for masses below the excluded range in large extra dimension models.
  • Sphaleron transitions remain rare enough that fewer than 0.34 percent of quark interactions above 9 TeV produce them.
  • Background processes fully account for all observed high-multiplicity events with no detectable new-physics contribution at current energies.
  • Higher-luminosity or higher-energy runs are required to test the same models at larger mass scales.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The limits shrink the viable parameter space for low-scale quantum gravity scenarios that rely on large extra dimensions.
  • The data-driven classification approach can be reused for other searches involving complex final states at future collider energies.
  • Continued non-observation would further delay experimental access to any Planck-scale physics that becomes visible only above 10 TeV.

Load-bearing premise

The kinematic features and phase-space proximity metric separate potential signals from background without introducing biases that depend on the specific models being tested.

What would settle it

An observed excess of events with high scalar sum of transverse momenta that matches the predicted multiplicity and energy distribution for black hole or sphaleron decays in the same dataset would falsify the exclusion.

Figures

Figures reproduced from arXiv: 2604.10732 by CMS Collaboration.

Figure 1
Figure 1. Figure 1: The ST (left) and sphericity (right) distributions for various BH (with n = 2) and sphaleron signal models are plotted along with the corresponding distributions for simulated QCD multijet background events. The distributions are normalized to unit area. in particle physics [68–72]. However, less attention has been given to the intrinsic geometry of the phase space manifold where scattering amplitudes are … view at source ↗
Figure 2
Figure 2. Figure 2: The SVM score distributions for simulated QCD multijets, and selected BH (with [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The SVM score vs. the ST distributions for simulated QCD multijet background (left) and the BH signal model B1 with MD = 2 TeV, MBH = 10 TeV, and n = 2 (right), after the S > 0.1 selection [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The ST distribution in the N ≥ 4 (left) and N ≥ 7 (right) in the SI-VR in data is indicated by the black dots. The background prediction is represented by the red line, and the gray band corresponds to the background modeling uncertainty. The lower panels show the difference between observed data and the background prediction, normalized by the total uncertainty. 7.2 Phase space distance method The backgro… view at source ↗
Figure 5
Figure 5. Figure 5: Post-fit ST distributions in VR-FAIL (left) and VR-PASS (right) regions in data. The gray hatched areas include both statistical and systematic uncertainties in the background pre￾diction (yellow histogram). The red line corresponds to the signal model B1, with MD = 2 TeV, MBH = 10 TeV, and n = 2. The lower panels show the difference between observed data and the background prediction, normalized by the to… view at source ↗
Figure 6
Figure 6. Figure 6: The ST distribution in the N ≥ 4 (left) and N ≥ 7 (right) SI-SR in data, indicated by the black dots, along with the background prediction and its uncertainty represented by the red line and gray band, respectively. Lower panel as in [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Expected and observed model-independent 95% CL upper limits on the cross section [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Post-fit ST distributions in the FAIL (left) and PASS (right) regions in data. The gray shaded area includes both statistical and systematic uncertainties in the background prediction (yellow histogram) while the red and blue lines are B1 signal examples, as noted in the legends. Lower panel as in [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Expected and observed 95% CL upper limits on the cross section for a semiclassical [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Excluded Mmin BH values as functions of MD and n for a variety of BLACKMAX (left) and CHARYBDIS2 (right) BH models. minimum black hole mass Mmin BH for different BH models. Upper limits on the number of extra dimensions n max are derived as the value of n at the intersection between the experimental limit curves and the theoretical cross sections, floored to the nearest integer. This limit is well￾defined… view at source ↗
Figure 11
Figure 11. Figure 11: Expected and observed 95% CL upper limits for SB models with [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Expected and observed 95% CL upper limits on the pre-exponential factor for the [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
read the original abstract

A search for microscopic black holes, string balls, and electroweak sphalerons using proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded with the CMS detector at the CERN LHC during the 2016$-$2018 data taking, and corresponding to an integrated luminosity of 138 fb$^{-1}$, is presented. Two search strategies based on control samples in data are used. Model-independent limits on the cross section of physics phenomena with multiple energetic jets, leptons, and photons are set using a method that relies on the shape invariance of the scalar sum of the transverse momenta of all objects in the event. Model-dependent limits on black hole and sphaleron production are set using a newly introduced method that has been developed for the identification of collider events with distinct kinematic features by separating them into classes based on phase space proximity. In the context of models with large extra dimensions, semiclassical black holes and string balls with masses below 8.4$-$11.4 TeV and 9.0$-$10.7 TeV, respectively, are excluded at 95% confidence level, significantly extending the reach beyond previous searches. Results of a dedicated search for electroweak sphalerons are used to derive an upper limit of 0.0034 at 95% confidence level on the fraction of quark-quark interactions above the nominal sphaleron transition energy threshold of 9 TeV.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper presents a search for microscopic black holes, string balls, and electroweak sphalerons in 13 TeV pp collisions recorded by CMS with 138 fb^{-1} of 2016-2018 data. Model-independent cross-section limits for multi-jet/lepton/photon final states are derived from the shape invariance of the scalar sum of transverse momenta in data control samples. Model-dependent limits on black hole/string ball production and on the sphaleron fraction are obtained via a new event classification technique that partitions events according to a phase-space proximity metric constructed from kinematic features. In large-extra-dimensions models, semiclassical black holes below 8.4-11.4 TeV and string balls below 9.0-10.7 TeV are excluded at 95% CL, and an upper limit of 0.0034 is set on the fraction of quark-quark interactions above the 9 TeV sphaleron threshold.

Significance. If the new classification method is shown to be robust, the results would extend existing mass limits on black holes and string balls by several TeV and provide the first dedicated constraint on the sphaleron transition fraction at the LHC. The consistent use of data-driven control samples for both the model-independent and model-dependent analyses is a methodological strength that reduces dependence on Monte Carlo modeling of backgrounds.

major comments (1)
  1. [Section describing the new event-classification method] The model-dependent exclusions (black holes 8.4-11.4 TeV, string balls 9.0-10.7 TeV, sphaleron fraction <0.0034) are obtained exclusively from the newly introduced phase-space proximity classification. The manuscript must supply quantitative validation (signal-injection closure tests, purity-efficiency curves, or background-shape stability checks) demonstrating that the kinematic metric separates signal from QCD/multijet background without model-dependent biases in the variables used for the limits.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. We address the major comment below and will update the paper to incorporate the requested validation.

read point-by-point responses

  1. Referee: [Section describing the new event-classification method] The model-dependent exclusions (black holes 8.4-11.4 TeV, string balls 9.0-10.7 TeV, sphaleron fraction <0.0034) are obtained exclusively from the newly introduced phase-space proximity classification. The manuscript must supply quantitative validation (signal-injection closure tests, purity-efficiency curves, or background-shape stability checks) demonstrating that the kinematic metric separates signal from QCD/multijet background without model-dependent biases in the variables used for the limits.

    Authors: We agree that quantitative validation of the phase-space proximity classification is essential to substantiate the model-dependent results. In the revised manuscript we will add a new subsection presenting signal-injection closure tests (injecting simulated black-hole, string-ball, and sphaleron events into data control samples and verifying unbiased recovery of the injected yields), purity-efficiency curves versus the proximity-metric threshold, and background-shape stability checks obtained by varying control-region definitions and metric parameters. These studies will explicitly demonstrate that the kinematic metric separates signal from QCD/multijet background without introducing model-dependent biases in the variables entering the limit-setting procedure. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's model-independent limits rely on shape invariance of scalar-sum distributions observed directly in data control samples, independent of any signal model or fitted parameters. Model-dependent limits normalize simulation to data without reducing the reported exclusions (black hole/string ball mass thresholds or sphaleron fraction) to any self-defined or fitted quantity by the paper's own equations. No self-definitional steps, fitted-input predictions, load-bearing self-citations, or ansatz smuggling are present; the new phase-space proximity classifier is an analysis tool whose validity is external to the limit-setting procedure itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard high-energy physics assumptions about background modeling and signal kinematics in large-extra-dimensions scenarios. No new particles or forces are postulated; the work constrains existing theoretical constructs using data-driven techniques.

axioms (1)
  • domain assumption Standard Model background processes are accurately modeled by Monte Carlo simulation and can be validated with data control samples.
    Invoked for both search strategies to establish the expected shape of the scalar-sum distribution in the absence of new physics.

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