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Observation of single top-quark production in the $s$ -channel in 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, the ATLAS collaboration reports the first single-experiment observation of single top-quark production in the $s$ -channel with a significance of 5.1 standard deviations, measuring a cross-section consistent with Standard Model predictions.

Original authors: ATLAS Collaboration

Published 2026-10-09

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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

In the subatomic world, matter is built from a small family of fundamental particles, among which the top quark holds a unique place. It is the heaviest of all known elementary particles, weighing nearly as much as a gold atom, yet it exists for only a fleeting instant before decaying. Because of its immense mass, the top quark interacts with the Higgs field more strongly than any other particle, making it a crucial probe for understanding how mass is generated in the universe. Physicists have long known that top quarks can be produced in two main ways: in pairs, where a top and its antimatter twin are created together, or singly, where a single top quark appears through a specific interaction involving the weak nuclear force. While the production of top-quark pairs has been observed for decades, and single top quarks produced via one specific weak-force pathway have been well documented, a third, rarer pathway has remained elusive. This final mode, known as the s-channel, involves a different arrangement of the weak force that is so suppressed in high-energy collisions that it has thus far evaded direct detection at the world's most powerful particle accelerator.

A researcher using the ATLAS detector at the Large Hadron Collider has finally captured evidence of this elusive process. By analyzing a vast collection of proton-proton collision data gathered over several years, corresponding to an integrated luminosity of 140 inverse femtobarns, the scientist was able to isolate the rare signal from a sea of background noise. The process they sought produces a single top quark alongside a bottom antiquark, which then decay into a specific set of particles: a single electron or muon, a burst of missing energy carried away by a neutrino, and exactly two jets of particles originating from bottom quarks. To distinguish this rare event from the overwhelming number of similar-looking events caused by other processes, they employed a sophisticated artificial intelligence tool known as a Graph Neural Network. This system treats each collision as a network of connected points, learning to recognize the subtle geometric and kinematic patterns that distinguish the rare s-channel signal from the common background.

The analysis yielded a clear result. The researcher observed a signal with a statistical significance of 5.1 standard deviations, a threshold that in particle physics is the formal requirement for claiming an observation. This means the likelihood that the observed signal is merely a random fluctuation of the background is less than one in three million. The team measured the rate at which these events occur, known as the cross-section, finding it to be 10.8 picobarns, with an uncertainty of roughly 1.5 picobarns from statistical limits and 1.6 picobarns from systematic experimental factors. This measured rate aligns closely with the theoretical prediction of 11.07 picobarns derived from the Standard Model of particle physics. The agreement between the observation and the prediction confirms that the Standard Model correctly describes this rare interaction, completing the experimental picture of all three known ways single top quarks are produced at the Large Hadron Collider.

This discovery is significant not only because it fills a gap in the experimental record but also because it provides a new, independent way to test the fundamental forces of nature. The s-channel process is directly sensitive to the strength of the interaction between the top quark and the bottom quark, a value encoded in a mathematical table known as the Cabibbo-Kobayashi-Maskawa matrix. Furthermore, because this process is so rare, it is highly sensitive to the presence of new, undiscovered particles or forces that might interfere with the interaction. By establishing a robust measurement of this suppressed process, the researcher has opened a new window for probing the electroweak sector of the Standard Model and searching for physics beyond our current understanding. The success of this measurement relied heavily on the ability to broaden the range of accepted collision events and to use advanced machine learning to separate the signal from the background, techniques that allowed them to achieve a sensitivity far greater than previous attempts. With this observation, the experimental search for single top quarks in the s-channel is complete, marking a milestone in the ongoing effort to map the fundamental structure of matter.

Technical Summary: Observation of Single Top-Quark Production in the $s$ -Channel

Problem and Context
Single top-quark production is a fundamental process in the Standard Model (SM) that proceeds via three distinct mechanisms: the $t$ -channel, associated $tW$ production, and the $s$ -channel. While the $t$ -channel and $tW$ modes have been firmly established at the Large Hadron Collider (LHC), the $s$ -channel has remained the last direct top-quark production mechanism to evade observation at the LHC. The $s$ -channel process is characterized by the exchange of a virtual $W$ boson between a quark and an antiquark, resulting in a single top quark and a bottom antiquark (or vice versa, $t\bar{b} + \bar{t}b$ ). This process is highly suppressed at the LHC because the leading-order mechanism requires a sea antiquark in the initial state, leading to a cross-section significantly smaller than that of top-quark pair ( $t\bar{t}$ ) production or $W$ +jets backgrounds. Previous ATLAS analyses at center-of-mass energies of 8 TeV and 13 TeV provided evidence for the process with significances of 3.2 and 3.3 standard deviations, respectively, but fell short of the 5 $\sigma$ threshold required for a formal observation.

Methodology
This analysis utilizes the full Run 2 dataset of proton–proton collisions collected by the ATLAS detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 140 fb $^{-1}$ . The selection strategy targets the semileptonic decay mode of the single top quark, requiring events with exactly one electron or muon, significant missing transverse momentum ( $E^{\text{miss}}_T$ ), and exactly two jets identified as originating from $b$ -quarks ( $b$ -tagged).

Key methodological advancements over previous ATLAS searches include:

Broadened Kinematic Acceptance: The selection criteria were relaxed to increase the number of available signal events by a factor of approximately three compared to the previous analysis.
Advanced $b$ -tagging: The GN2 algorithm, utilizing a graph transformer architecture, was employed to identify $b$ -jets with an 85% efficiency working point in dileptonic $t\bar{t}$ events.
Graph Neural Network (GNN): A GNN was developed to discriminate the $s$ -channel signal from the dominant backgrounds ( $t\bar{t}$ , $W$ +jets, and $t$ -channel single top). The network models each event as a fully connected graph where the lepton, two $b$ -tagged jets, and $E^{\text{miss}}_T$ serve as nodes. Edges encode kinematic relationships ( $\Delta\phi$ , $\Delta\eta$ , $\Delta R$ , $\Delta p_T$ , and invariant mass). The GNN was trained as a binary classifier to separate the signal from all background processes, achieving superior signal-to-background separation compared to previous methods.
Statistical Analysis: A binned profile maximum-likelihood fit was performed simultaneously across the Signal Region (SR) and orthogonal Control Regions (CRs) for $t\bar{t}$ , $W$ +jets, and multijet backgrounds. The GNN output score served as the discriminating variable in the SR and $W$ +jets CR, while the scalar sum of transverse momenta ( $H_T$ ) was used in the $t\bar{t}$ CR. Systematic uncertainties, including those from detector calibration, background modeling, and theoretical predictions (PDFs, renormalization/factorization scales), were incorporated as nuisance parameters.

Key Results
The analysis yields an observed signal significance of 5.1 standard deviations, with an expected significance of 5.2 standard deviations, constituting the first single-experiment observation of single top-quark production in the $s$ -channel at the LHC.

The measured inclusive cross-section for $s$ -channel production ( $t\bar{b} + \bar{t}b$ ) is:
$\sigma_{t\bar{b}+\bar{t}b} = 10.8 \pm 1.5 \text{ (stat.)} \pm 1.6 \text{ (syst.) pb}$
This result is consistent with the Standard Model prediction of $11.07^{+0.19}_{-0.18}$ pb, calculated at next-to-next-to-leading-order (NNLO) in QCD. The total uncertainty is approximately 20.4%, with systematic and statistical uncertainties contributing roughly equally (15.2% and 13.5%, respectively). The leading systematic uncertainties arise from background modeling (specifically $tW$ and $t\bar{t}$ interference and $W$ +jets modeling) and jet calibration.

Significance
The paper claims that this result establishes the observation of the $s$ -channel process, completing the experimental observation of all three single top-quark production mechanisms at the LHC. Beyond this milestone, the measurement provides a crucial, independent validation of the electroweak sector of the Standard Model. By establishing a robust measurement of this suppressed process, the analysis opens a new phase space to directly probe the top quark's electroweak couplings and constrain physics beyond the Standard Model. Specifically, the measurement offers sensitivity to heavy resonances in the $s$ -channel, such as $W'$ bosons or charged Higgs bosons, and allows for constraints on anomalous couplings via effective field theories. The improved sensitivity achieved through the broadened kinematic acceptance and the introduction of the GNN overcomes the immense background challenges that previously hindered direct detection at these collision energies.

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