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Observation of pair production of longitudinally polarized $Z$ bosons in four-lepton final state with the ATLAS detector

Using 13.6 TeV proton-proton collision data from the ATLAS experiment, researchers measured the production of two longitudinally polarized $Z$ bosons and, by combining these results with previous 13 TeV data, achieved the first observation of this process with a significance of 6.5 standard deviations.

Original authors: ATLAS Collaboration

Published 2026-07-15

📖 5 min read🧠 Deep dive

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

Imagine the universe as a giant, high-speed dance floor where tiny particles zoom around, bumping into each other at speeds close to the speed of light. At the Large Hadron Collider (LHC), scientists are the ultimate dance critics, watching these collisions to see how the particles move and spin. One of the most important moves in this cosmic dance is called "polarization," which is just a fancy word for the direction a particle is spinning or pointing as it flies.

For decades, physicists have been trying to understand a mysterious force called the "Higgs field" (the thing that gives particles their mass). This field is like a thick, invisible syrup that slows particles down. When particles move through this syrup, they can end up spinning in different ways: some spin sideways (transverse), and some spin head-on (longitudinal). The rules of the Standard Model—the universe's best instruction manual—predict exactly how many particles should be spinning head-on. If the manual is wrong, it means there's a secret new rulebook we haven't found yet.

The Big Discovery
In this new study, the ATLAS team, a massive group of scientists working with a giant detector called ATLAS, decided to count the dancers. They looked at data from 164 billion billion collisions (164 fb⁻¹) that happened at a super-high energy of 13.6 TeV. They were specifically hunting for a rare event: two Z bosons (heavy particles that act like messengers of the weak force) appearing together, both spinning head-on (longitudinally) at the same time.

Think of it like trying to spot two people in a crowded stadium who are both doing a specific, difficult handstand at the exact same moment. It's rare, and it's hard to see because most people are just standing or walking.

What They Found
The team found the evidence they were looking for. They measured the "signal strength" (how much of this head-on spinning they saw compared to what the manual predicted) to be 1.34 ± 0.29. This number is very close to 1.00, which is what the Standard Model predicted.

When they combined these new results with an older study they did at 13 TeV, the evidence became even stronger. The final result showed that the production of two simultaneously head-on spinning Z bosons is a real thing, with a significance of 6.5 standard deviations. In the world of particle physics, 5 standard deviations is the "gold standard" for claiming a discovery. It's like flipping a coin and getting heads 6.5 times in a row when you only expected it to happen once in a million tries. The team expected to see 5.6 standard deviations, and they saw 6.5.

What They Ruled Out
The paper doesn't rule out the Standard Model; in fact, it confirms it! The results are consistent with the predictions. However, the study explicitly rules out the idea that this specific "double head-on" event is just a fluke or a mistake in the data. They also treated a specific background process (gluon fusion, where two gluons smash together to make Z bosons) as a "background noise" to be safe, rather than trying to measure its polarization directly, because the tools to do that perfectly aren't ready yet. This means they are being extra careful not to claim they found something new if it's just a glitch in the simulation.

How Sure Are They?
The scientists are extremely confident. They didn't just guess; they measured it.

They observed the event with a significance of 6.5 standard deviations.
They measured the fraction of these events to be 0.080 ± 0.017 (meaning about 8% of the time, the Z bosons were both spinning head-on).
They measured the cross-section (the probability of this happening) to be 2.30 ± 0.49 fb.

The paper states that the measurement is limited mostly by the amount of data they have (statistical uncertainty), not by a lack of understanding of the equipment. The biggest "worry" in their numbers comes from the theoretical models used to predict how the particles should behave, but even with that uncertainty, the result holds up.

The Takeaway
This paper is a victory lap for the Standard Model. It confirms that the "syrup" of the Higgs field works exactly as the manual says it should, even in these rare, high-energy collisions where two Z bosons decide to spin head-on together. While the scientists are thrilled to have "observed" this phenomenon (which means they are 99.9999% sure it's real), they aren't claiming to have found a new particle or a new force. Instead, they've successfully checked a very specific, difficult box on the universe's instruction manual and found that the instructions are correct.

In short: The universe is spinning exactly as the experts predicted, and the ATLAS team has finally caught two Z bosons doing the perfect head-on spin together, proving that the rules of the game are holding up under the most intense pressure.

Technical Summary: Observation of Pair Production of Longitudinally Polarized Z Bosons

Problem and Motivation
Following the discovery of the Higgs boson, the scrutiny of Electroweak Symmetry Breaking (EWSB) has become a primary focus at the Large Hadron Collider (LHC). The EWSB mechanism generates the masses of the $W$ and $Z$ bosons and gives rise to their longitudinal polarization states. While precise polarization measurements have been performed for single bosons and in $WZ$ production, the joint-polarization states of pairs of weak bosons remain a critical test of the EWSB mechanism. Specifically, the production of two simultaneously longitudinally polarized $Z$ bosons ( $Z_L Z_L$ ) is predicted to be strongly suppressed relative to transverse modes at high invariant masses due to the Goldstone Boson Equivalence Theorem. Measuring the dependence of the longitudinal-longitudinal (LL) component as a function of the diboson invariant mass provides a sensitive probe for deviations from the Standard Model (SM). Previous ATLAS results provided evidence for $Z_L Z_L$ production with a significance of 4.3 standard deviations ( $\sigma$ ); this work aims to achieve the first observation of this process.

Methodology
The analysis utilizes proton–proton collision data recorded by the ATLAS detector at a center-of-mass energy of $\sqrt{s} = 13.6$ TeV, corresponding to an integrated luminosity of 164 fb $^{-1}$ . The study focuses on the four-lepton final state ( $ZZ \to \ell^+\ell^-\ell'^+\ell'^-$ ), where $\ell, \ell'$ are electrons or muons.

Event Selection: Events are reconstructed using two same-flavor, opposite-charge (SFOC) lepton pairs. Candidate events require four baseline leptons, with the two highest- $p_T$ leptons satisfying $p_T > 27$ and 20 GeV. Two $Z$ boson candidates are formed from SFOC pairs with invariant masses within $|m_{\ell\ell} - m_Z| < 10$ GeV. The four-lepton invariant mass ( $m_{4\ell}$ ) must exceed 180 GeV.
Signal Regions (SR): The SR is split into two categories based on $m_{4\ell}$ to exploit kinematic differences between polarization components: a low-mass region ( $180 < m_{4\ell} < 240$ GeV) and a high-mass region ( $m_{4\ell} > 240$ GeV).
Background Estimation: Irreducible backgrounds (e.g., $t\bar{t}Z$ , tri-boson) are estimated using Monte Carlo (MC) simulations. Reducible backgrounds from non-prompt leptons are estimated using a data-driven fake-factor method. The inclusive $gg \to ZZ$ process is treated as a background to remain conservative, given discrepancies observed in reweighting methods for polarized gluon fusion.
Polarization Extraction: A Boosted Decision Tree (BDT) is trained to separate $Z_L Z_L$ production from $Z_T Z_X$ (transverse-transverse or transverse-longitudinal) states. Input variables include angular observables sensitive to polarization, such as azimuthal angles between leptons and decay angles in the $Z$ rest frames.
Statistical Analysis: A binned profile likelihood fit is performed on the BDT score distribution in both SRs simultaneously. The signal strengths $\mu_{LL}$ (for $Z_L Z_L$ ) and $\mu_{TX}$ (for $Z_T Z_X$ ) are extracted as free parameters. The interference term between polarization states is modeled as proportional to $\sqrt{\mu_{LL}\mu_{TX}}$ . Systematic uncertainties, including theoretical modeling (PDFs, scales, parton showering) and experimental effects, are incorporated as nuisance parameters.
Combination: The Run 3 results are statistically combined with the previous Run 2 measurement at $\sqrt{s} = 13$ TeV (140 fb $^{-1}$ ), ensuring consistent treatment of backgrounds, interference templates, and theoretical uncertainties.

Key Contributions and Results

First Observation of $Z_L Z_L$ : By combining Run 2 and Run 3 data, the collaboration reports the first observation of the production of two simultaneously longitudinally polarized $Z$ bosons. The observed significance is 6.5 $\sigma$ , with an expected significance of 5.6 $\sigma$ .
Signal Strength Measurement: In the combined fit, the signal strength for $Z_L Z_L$ production is measured to be $\mu_{LL} = 1.22 \pm 0.21$ . This is consistent with the SM prediction of $\mu_{LL} = 1.00$ .
Fiducial Cross-Section and Fraction:
- The fiducial cross-section for $Z_L Z_L$ production is measured as $\sigma_{obs} = 2.30 \pm 0.49$ fb, consistent with the SM prediction of $1.71 \pm 0.11$ fb.
- The inclusive fraction of $Z_L Z_L$ events is measured to be $f_{LL} = 0.080 \pm 0.017$ , consistent with the SM prediction of $0.061 \pm 0.002$ .
- Differential measurements in the low-mass and high-mass SRs yield $f_{LL}^{low} = 0.108 \pm 0.028$ and $f_{LL}^{high} = 0.011 \pm 0.017$ , respectively, both consistent with SM expectations.
Methodological Refinements: The analysis introduces a more conservative treatment of the $gg \to ZZ$ process as a background and utilizes updated theoretical templates (Sherpa 3) for interference modeling, addressing discrepancies found in previous reweighting approaches.

Significance
The paper claims that this result constitutes the first observation of the pair production of longitudinally polarized $Z$ bosons. This measurement validates the SM prediction regarding the generation of longitudinal polarization states via EWSB in a diboson system. The results are consistent with Standard Model predictions across the fiducial phase space and in differential regions of the four-lepton invariant mass. The observation confirms the theoretical understanding that the longitudinal component, while suppressed at high energies, is present and measurable, providing a crucial test of the mechanism that generates the masses of the weak bosons. The statistical combination of Run 2 and Run 3 data was essential to reach the 5 $\sigma$ observation threshold.

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