⚛️ phenomenology

Impact of neutral fluxes and signal significance optimization on semi-exclusive $pp \to t\bar{t}$ production via deep learning training

This paper demonstrates that deep learning techniques combined with updated flux models can effectively discriminate semi-exclusive $t\bar{t}$ production from background, predicting a $5\sigma$ discovery significance for both photon- and pomeron-induced processes at the LHC with modest integrated luminosities.

Original authors: A. Cota Rodríguez, Jesús Alberto V. Corral, J. A. Murillo Quijada

Published 2026-09-24

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CC BY 4.0

Original authors: A. Cota Rodríguez, Jesús Alberto V. Corral, J. A. Murillo Quijada

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

In the subatomic world, particles rarely travel alone. When protons smash together at nearly the speed of light, they shatter into a chaotic spray of new particles, a process governed by the strong nuclear force. However, nature also allows for a quieter, more elusive interaction. Sometimes, protons can exchange invisible messengers without breaking apart completely. One such messenger is the photon, a particle of light that carries electromagnetic force. The other is the pomeron, a theoretical object that carries the strong force but behaves like a ghostly, neutral entity that leaves the protons largely intact. These rare events, where the protons survive the collision but exchange energy to create heavy new particles, are called semi-exclusive. Physicists are eager to find them because they offer a pristine window into the fundamental structure of matter, free from the messy debris that usually obscures such interactions. Yet, spotting these faint signals amidst the overwhelming noise of standard collisions has remained one of the most difficult challenges in high-energy physics.

A team of researchers has now taken a significant step toward solving this puzzle by simulating how these rare events would look inside the Large Hadron Collider, the massive machine at CERN that smashes protons together. Using powerful computer models, they recreated the conditions of these collisions to see if they could distinguish the quiet, semi-exclusive events from the loud, chaotic background of ordinary particle production. Their work focused on the creation of top quarks, the heaviest known elementary particles, which are notoriously difficult to produce in these gentle, semi-exclusive ways. The team employed a sophisticated form of artificial intelligence, known as a deep neural network, to act as a filter. This digital brain was trained to recognize the subtle fingerprints of the rare events, learning to ignore the overwhelming noise of standard collisions by focusing on specific patterns in the detector data.

The researchers discovered that the key to finding these events lies in what is missing rather than what is present. In a standard collision, the debris spreads out evenly in all directions. In the rare semi-exclusive events, however, a large empty region appears on one side of the detector, a gap where no particles are found. This happens because the protons exchange energy without shattering, leaving a clean path for the debris to travel in the opposite direction. The team found that the most effective way to spot this gap was by measuring the lowest amount of energy detected in the forward section of the machine, the area closest to the beam line. If this minimum energy is very low, it strongly suggests that a rare, semi-exclusive event has occurred. By using this specific measurement as a primary clue, their artificial intelligence model achieved an exceptional level of accuracy, correctly identifying the rare photon-induced events with a performance score of nearly 0.99 on a scale where 1.0 is perfect.

The study also revealed how these events change as the energy of the collisions increases. When the researchers simulated the conditions of the current Large Hadron Collider and compared them to the much higher energies expected at a future machine called the Future Circular Collider, they saw a dramatic rise in the number of these events. The rate of production for events driven by the pomeron increased by a factor of about fifty, while those driven by photons increased by a factor of about twenty-two. This suggests that as we build more powerful machines, these rare interactions will become much more common, making them easier to study. However, the team also highlighted a significant source of uncertainty. While the photon-based events are relatively well understood, the pomeron is a more complex theoretical object, and different ways of modeling it led to variations in the predicted number of events. This uncertainty is much larger for the pomeron than for the photon, reflecting the fact that our understanding of the pomeron's internal structure is still incomplete.

Despite these uncertainties, the results are promising for future experiments. The team calculated that with a relatively small amount of data, equivalent to just one year of running at the current machine, it should be possible to confirm the existence of the pomeron-driven events with high statistical certainty. For the photon-driven events, a slightly larger dataset would be needed to reach the same level of confidence. The study concludes that these rare top quark pairs are within reach of current and near-future experiments, provided that scientists can effectively use the forward detectors to measure those empty gaps and low-energy signals. This work lays a crucial foundation for the next generation of searches, offering a clear path to observing these elusive interactions and deepening our understanding of the forces that hold the universe together.

Technical Summary: Impact of Neutral Fluxes and Signal Significance Optimization on Semi-Exclusive $pp \to t\bar{t}$ Production via Deep Learning Training

Problem Statement
The paper addresses the challenge of identifying semi-exclusive top-antitop ( $t\bar{t}$ ) production in proton-proton ($pp$) collisions at the Large Hadron Collider (LHC) and Future Circular Collider (FCC). Unlike standard inclusive production, semi-exclusive events involve the exchange of neutral color-singlet objects—specifically photons ( $\gamma$ ) or pomerons ( $P$ )—where one proton remains intact ( $p'$ ) and the other dissociates, resulting in a final state of $p' t\bar{t} X$ . These processes are theoretically significant as probes of Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) in non-perturbative regimes and for studying the internal partonic structure of the pomeron. However, these signals are predicted to have cross-sections orders of magnitude smaller than the dominant non-peripheral $t\bar{t}X$ background (mediated by color exchange). Furthermore, theoretical predictions for these processes suffer from significant uncertainties due to the phenomenological modeling of pomeron fluxes and parton distribution functions (DPDFs), as well as photon flux parameterizations. The primary problem is determining how these modeling uncertainties impact physical observables and whether a statistically significant observation is feasible using forward physics observables and machine learning techniques without relying solely on forward proton tagging.

Methodology
The authors employed a multi-stage simulation and analysis framework:

Monte Carlo Simulation:
- Generators: Events were generated using MadGraph5_aMC@NLO (for photon-induced processes at NLO) and PYTHIA8 (for showering, hadronization, and pomeron-induced processes).
- Flux and Structure Models:
  - Pomeron-induced: The Ingelman-Schlein formalism was used, implementing various data-driven flux parameterizations (e.g., Schuler-Sjöstrand) and DPDF sets (H1 2006 Fit A/B, LO/NLO). Five distinct pomeron schemes were tested to quantify systematic uncertainties.
  - Photon-induced: The Equivalent Photon Approximation (EPA) was applied using the Weizsäcker-Williams, Budnev, and Drees-Zeppenfeld models.
- Energy Regimes: Simulations covered $\sqrt{s} = 13$ TeV (LHC) and projected up to 100 TeV (FCC).
Detector Simulation and Reconstruction:
- Events were processed through Delphes 3 using the CMS detector configuration.
- Selection Criteria: A semi-leptonic $t\bar{t}$ decay channel was selected ( $N_{jets} \geq 2$ , $N_{b-jets} \geq 1$ , $N_{lepton} = 1$ , $E_T^{miss} > 20$ GeV).
- Observables: Key discriminators included charged particle multiplicity ( $N_{ch}$ ), forward rapidity gaps (FRG), and forward calorimetric energy deposits (specifically the Hadronic Forward (HF) region, $3.0 \leq |\eta| \leq 5.0$ ).
Machine Learning Classification:
- A feed-forward neural network (TensorFlow/Keras) was trained to distinguish between photon-induced, pomeron-induced, and non-peripheral background events.
- Input Features: Nine observables were used, including jet multiplicity, $N_{ch}$ , FRG, and various HF energy sums (e.g., minimum HF tower energy).
- Performance: The network was evaluated using Area Under the Curve (AUC), accuracy, and Kolmogorov-Smirnov (KS) statistics.
Statistical Inference:
- A profile-likelihood fit was performed using the Combine framework on Asimov datasets.
- Signal strengths ( $\mu$ ) were extracted for both production modes.
- Systematic uncertainties arising from the choice of flux/structure models were propagated as "scheme-dependent" systematics.

Key Contributions and Results

Cross-Section Scaling: The study predicts a substantial increase in semi-exclusive cross-sections from LHC to FCC energies. The pomeron-induced cross-section rises by a factor of $\sim 50$ , and the photon-induced by $\sim 22$ , when moving from 13 TeV to 100 TeV. The ratio of pomeron-to-photon rates increases from 8.6 at 13 TeV to nearly 20 at 100 TeV, driven by the rapid growth of gluon densities in the pomeron.
Model Dependence and Uncertainties:
- The total cross-section for pomeron-induced production exhibits a systematic variation of up to 62.5% depending on the chosen flux and DPDF scheme (dominated by the H1-AB-LO scheme).
- Photon-induced production shows a much smaller systematic variation of 9.2% across different flux models.
- These variations translate directly to the signal strength uncertainty, with the pomeron channel having a systematic contribution of 25.1% and the photon channel 7.6% to the total uncertainty.
Kinematic Observables:
- Rapidity Gaps: Semi-exclusive events exhibit significantly larger forward rapidity gaps compared to non-peripheral backgrounds. For photon-induced events, 41.07% of events have a gap size $\geq 1.0$ , compared to 0.07% for the background.
- Multiplicity: Semi-exclusive events have lower charged-particle multiplicities ( $N_{ch}$ ). 47.6% of photon-induced and 28.8% of pomeron-induced events have $N_{ch} < 50$ , versus only 6.7% for the background.
- Best Discriminator: At the detector level, the minimum Hadronic Forward (HF) tower energy was identified as the most effective single variable for discrimination, achieving the highest KS test scores against the background.
Deep Learning Performance:
- The neural network achieved an AUC of 0.9917 ± 0.0002 for distinguishing photon-induced signals from non-peripheral backgrounds.
- Separation between photon and pomeron signals was also strong (AUC $\approx$ 0.945), while separating pomeron from background was slightly lower (AUC $\approx$ 0.879) due to the shared semi-exclusive topology.
Significance Projections:
- Assuming low pile-up conditions and using Asimov datasets:
  - Pomeron-induced: A $5\sigma$ significance is expected with an integrated luminosity of 1 fb $^{-1}$ .
  - Photon-induced: A $5\sigma$ significance is expected with 4.7 fb $^{-1}$ .
- At 4.7 fb $^{-1}$ , the expected 95% confidence level intervals for the signal strengths are $\mu_\gamma \in [0.716, 1.287]$ and $\mu_P \in [0.883, 1.118]$ .

Significance and Claims
The paper claims that the observation of semi-exclusive $t\bar{t}$ production is feasible using existing Run 2 and Run 3 LHC data, provided that forward physics observables and deep learning techniques are utilized. A primary contribution is the demonstration that proton tagging is not strictly necessary to achieve discovery-level separation; instead, forward calorimetry (specifically HF energy and rapidity gaps) combined with multivariate analysis can effectively suppress the non-peripheral background.

The authors highlight that while the pomeron-induced channel offers a higher event yield, it is subject to significantly larger theoretical uncertainties (flux and structure function modeling) compared to the photon-induced channel. The study establishes a phenomenological framework to estimate the luminosity required for a $5\sigma$ observation at both LHC and FCC energies, serving as a guide for future experimental searches within the LHC forward physics program. The work underscores the potential of semi-exclusive top production as a laboratory for studying color-singlet exchange mechanisms and the interplay between QCD and QED dynamics.

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