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Measurement of $tZq$ inclusive and differential cross-sections in $pp$ collisions at $\sqrt{s} = 13~\text{TeV}$ with the ATLAS detector

Using 140 fb⁻¹ of proton-proton collision data at 13 TeV collected by the ATLAS detector, this paper presents the first measurement of the inclusive and differential cross-sections for the $tZq$ process in the trilepton channel, finding results consistent with Standard Model predictions and setting constraints on dimension-6 effective field theory operators.

Original authors: ATLAS Collaboration

Published 2026-08-27

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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 vast, high-energy collisions occurring deep within the Large Hadron Collider, physicists are constantly searching for the rarest and most elusive events. Among the most fascinating of these are processes involving the top quark, the heaviest known elementary particle, which exists for only a fraction of a second before decaying into other particles. Sometimes, this top quark is produced alone, rather than in pairs, and in a specific type of interaction known as the t-channel, it is accompanied by a Z boson, a particle that carries the weak nuclear force. This specific combination, a single top quark and a Z boson, is a rare occurrence that acts as a sensitive probe for the fundamental rules governing how matter interacts. Because this process happens purely through the weak force, it offers a clean laboratory to test the Standard Model, the prevailing theory of particle physics, and to look for any subtle signs of new physics that might lie beyond our current understanding.

A researcher using the ATLAS detector has now performed the most precise measurement to date of this rare event. By analyzing a massive dataset of proton-proton collisions recorded between 2015 and 2018, corresponding to an integrated luminosity of 140 inverse femtobarns, they were able to isolate and count these specific interactions. The challenge was immense, as the signal they sought was buried under a sea of more common background events. To find it, they focused on a specific signature: events where the collision produced three light leptons (electrons or muons) and several jets of particles, with at least one jet originating from a bottom quark. This unique combination of three charged particles and specific jet patterns allowed them to filter out the noise and identify the rare t-channel production of a top quark and a Z boson.

The researcher measured the rate at which these events occur, known as the cross-section, and found it to be 95.2 femtobarns. This result, which includes both statistical and systematic uncertainties, aligns perfectly with the most advanced predictions of the Standard Model. The measurement was precise enough to separate the production of top quarks from the production of their antimatter counterparts, top antiquarks, and to determine the ratio between them. This ratio is particularly important because it depends on the internal structure of the proton, specifically the distribution of quarks within it. The measured ratio was found to be consistent with theoretical expectations, providing further confirmation that our understanding of how protons are built is correct.

Beyond simply counting the events, they looked at the detailed kinematics of the collision to see how the particles moved and interacted. They measured how the energy and direction of the particles varied, creating a detailed map of the process at both the level of the raw particles and the level of the stable particles that reach the detector. These differential measurements allow physicists to test the theory under different conditions, such as when the particles are produced with very high energy. The data matched the theoretical predictions across all these different variables, showing no significant deviations that would hint at new forces or particles.

The study also explored the spin properties of the top quark, a quantum characteristic that describes how the particle rotates. By analyzing the angles at which the decay products were emitted, they calculated a spin asymmetry value of 0.34. This number, which describes a preference for the top quark to be produced with a specific orientation, was found to be in good agreement with the Standard Model prediction. This result confirms that the mechanisms producing these heavy particles behave exactly as the current theory dictates, even when subjected to the intense scrutiny of a high-precision measurement.

Finally, they used their findings to constrain the Standard Model Effective Field Theory, a framework used to search for new physics by looking for small deviations in how particles interact. They examined nine different parameters that could potentially alter the behavior of the top quark and the Z boson. The analysis revealed no evidence of such deviations, placing tight limits on the possible influence of these hypothetical effects. The results confirm that, within the precision of this experiment, the behavior of the top quark and the Z boson is fully consistent with the established laws of physics. This comprehensive study not only refines our knowledge of a rare process but also sets a new benchmark for future searches for physics beyond the Standard Model.

Technical Summary: Measurement of $tZq$ Inclusive and Differential Cross-Sections in $pp$ Collisions at $\sqrt{s}=13$ TeV with the ATLAS Detector

Problem and Motivation
This paper presents a measurement of the electroweak production of a single top quark in association with a $Z$ boson in the $t$ -channel ( $tZq$ ) using the full Run 2 dataset of the ATLAS experiment. While the $tZq$ process was previously observed by ATLAS and CMS, this analysis aims to improve the precision of the measurement and provide the first differential cross-section measurements for this process at both particle and parton levels using ATLAS data. The process is of particular interest because, unlike $t\bar{t}Z$ production which involves strong interactions at leading order (LO), $tZq$ proceeds purely via electroweak interactions at LO. This makes it a sensitive probe for deviations from the Standard Model (SM) within the framework of the Standard Model Effective Field Theory (SMEFT), particularly for dimension-six operators affecting top-quark electroweak couplings. Furthermore, precise characterization of $tZq$ is essential as it constitutes a significant background to the rare $tHq$ process.

Methodology
The analysis utilizes proton-proton collision data collected between 2015 and 2018 at a center-of-mass energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 140 fb $^{-1}$ .

Event Selection: The measurement focuses on the trilepton final state ( $pp \to t\ell^+\ell^-q$ ), where the $Z$ boson decays into an electron or muon pair ( $m_{\ell\ell} > 30$ GeV) and the top quark decays leptonically. Events are selected requiring exactly three light leptons ( $e$ or $\mu$ ), missing transverse momentum, and two to four jets, with one or two identified as $b$ -jets. The selection includes both resonant $Z$ -boson production and non-resonant dilepton production.
Background Estimation: The dominant backgrounds are $t\bar{t}Z$ , diboson ( $VV$ ) production, and events with non-prompt or "fake" leptons (NPL). A semi-data-driven "template fit method" is employed to estimate NPL backgrounds, utilizing control regions enriched in heavy-flavor decays and $Z$ +jets events. Dedicated control regions (CRs) are defined for $t\bar{t}Z$ (requiring $\ge 5$ jets) and $VV$ +jets (vetoing $b$ -tagged jets) to constrain background normalizations.
Multivariate Analysis: A neural network (NN) discriminant is trained to separate the $tZq$ signal from backgrounds. The NN utilizes 19 input variables, including kinematic properties of the spectator jet (which is characteristic of the $t$ -channel topology), $b$ -tagging scores, and angular distances.
Measurement Strategy:
- Inclusive Cross-Section: A binned profile-likelihood fit is performed on the NN discriminant distribution in the signal region (SR) and control regions. The fit extracts the signal strength and normalizations for dominant backgrounds.
- Differential Cross-Sections: Unfolding is performed using a profile-likelihood unfolding (PLU) method to correct for detector resolution and acceptance effects. Measurements are provided at both the particle level (fiducial volume matching detector selection) and parton level (inclusive of final-state radiation).
- Spin Asymmetry: The top-quark spin asymmetry is extracted from the unfolded distribution of the top-quark polarisation angle ( $\cos \theta^*$ ) in the top-quark rest frame.
- SMEFT Interpretation: Detector-level distributions of the reconstructed $Z$ -boson transverse momentum ( $p_T(Z)$ ) are interpreted in the SMEFT framework. Nine Wilson coefficients corresponding to seven dimension-six operators in the Warsaw basis are constrained.

Key Contributions

Improved Precision: The inclusive cross-section measurement achieves a total uncertainty of 10%, an improvement over previous ATLAS results, driven by a looser event selection to increase signal acceptance and improved object reconstruction (including particle-flow jets and updated $b$ -tagging).
First Differential Measurements: This work presents the first differential cross-section measurements for $tZq$ production at both particle and parton levels using ATLAS data, covering observables such as $p_T(Z)$ , $|\eta(Z)|$ , $p_T(t)$ , spectator jet kinematics, and the top-quark spin asymmetry.
Separate Top/Top-Antitop Measurements: The analysis separately measures the cross-sections for top-quark ( $tZq(t)$ ) and top-antiquark ( $tZq(\bar{t})$ ) production and their ratio, providing sensitivity to proton parton distribution functions (PDFs).
SMEFT Constraints: The results provide constraints on SMEFT Wilson coefficients, leveraging the complementary sensitivity of $tZq$ and $t\bar{t}Z$ processes to resolve degeneracies in the parameter space.

Results

Inclusive Cross-Section: The measured inclusive cross-section for $m_{\ell\ell} > 30$ GeV is $\sigma(tZq) = 95.2^{+8.5}_{-7.9} \text{ (stat.) } ^{+5.5}_{-5.3} \text{ (syst.) fb}$ . This is in good agreement with the SM prediction of $84.0^{+4.7}_{-1.0}$ fb (5FS NLO QCD).
Separate Cross-Sections and Ratio:
- $\sigma(tZq(t)) = 56.0^{+6.2}_{-5.6} \text{ (stat.) } ^{+3.6}_{-3.4} \text{ (syst.) fb}$
- $\sigma(tZq(\bar{t})) = 39.3^{+5.9}_{-5.3} \text{ (stat.) } ^{+3.1}_{-3.0} \text{ (syst.) fb}$
- Ratio $R_t = 1.42^{+0.27}_{-0.22} \text{ (stat.) } \pm 0.05 \text{ (syst.)}$ , consistent with the SM prediction of 1.79.
Differential Measurements: The unfolded differential cross-sections for various kinematic variables are found to be well-described by SM predictions (MadGraph5_aMC@NLO + Pythia 8) in both 4FS and 5FS schemes. The statistical uncertainty dominates the differential measurements.
Spin Asymmetry: The top-quark spin asymmetry is measured to be $A = 0.34 \pm 0.14 \text{ (stat.) } \pm 0.06 \text{ (syst.)}$ , consistent with the SM prediction.
SMEFT Limits: Constraints are set on nine Wilson coefficients. No significant deviation from the SM is observed. The constraints on $C^{(1)}_{HQ}$ , $C^{(3)}_{HQ}$ , and $C^{(3,1)}_{Qq}$ are comparable to existing ATLAS limits, while other operators show no improvement due to limited statistical sensitivity.

Significance
The author states that these measurements constitute the most precise ATLAS study of $tZq$ production to date. The results provide a comprehensive test of the electroweak interactions of the top quark and serve as valuable input for future global SMEFT interpretations. The differential measurements and the separation of top and top-antitop contributions offer enhanced sensitivity to the underlying production dynamics and parton distribution functions, while the SMEFT interpretation demonstrates the complementarity of $tZq$ and $t\bar{t}Z$ processes in constraining new physics parameters.

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