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Electroweak WZ production shows first evidence of longitudinally polarised Z bosons, at 4.0 sigma, with a measured fraction matching the Standard Model.

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2026-08-01 10:21 UTC pith:XJKWGEZP

load-bearing objection First WZjj-EW polarisation-fraction extraction; a solid, stat-dominated 4.0σ result whose main caveat—MC-fixed non-measured fractions—is real but likely second-order. the 1 major comments →

arxiv 2607.20246 v1 pith:XJKWGEZP submitted 2026-07-22 hep-ex

Evidence for longitudinally polarised Z bosons in electroweak W^(pm)Z production in association with two jets from pp collisions at sqrt{s} = 13 TeV and 13.6 TeV with the ATLAS detector

ATLAS Collaboration This is my paper
classification hep-ex
keywords polarisation fractionslongitudinally polarised Z bosonelectroweak WZjj productionvector-boson scatteringneural networkprofile-likelihood fitLHCStandard Model
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper sets out to show that, in the rare electroweak process in which a W and a Z boson are produced together with two tagging jets (WZjj-EW) — the second most accessible vector-boson scattering channel at the LHC — a measurable fraction of the Z bosons spin along their line of flight, i.e. are longitudinally polarised. Using 304 fb^{-1} of proton–proton collision data at 13 and 13.6 TeV, the analysis extracts three polarisation fractions with dedicated neural-network discriminants and a profile-likelihood fit. The central claim is that longitudinally polarised Z bosons are present in the data with a significance of 4.0 standard deviations, and that their fraction, f_X0 = 0.32 ± 0.09, agrees with the Standard Model prediction at next-to-leading electroweak order, f_X0 = 0.2745 ± 0.0008. No evidence is found for longitudinally polarised W bosons, and upper limits are placed on the fractions f_0X and f_00. If correct, this is the first evidence for longitudinal polarisation of the Z in electroweak WZjj production, a direct probe of the electroweak symmetry-breaking mechanism.

Core claim

On its own terms, the paper establishes that in the fiducial phase space of WZjj-EW production (leptonic W and Z decays, two tagging jets with m_jj > 500 GeV), the fraction of events in which the Z boson is longitudinally polarised, regardless of the W polarisation, is f_X0 = 0.324 ± 0.088 after the combined Run 2 + Run 3 fit. The hypothesis that no such events exist is rejected at 4.0 standard deviations (2.9 expected). This value is compatible with the NLO-EW prediction of 0.2745 ± 0.0008 from the fixed-order calculation. The paper also reports upper limits of 0.19 and 0.12 at 95% CL on the fractions of events with a longitudinal W boson (f_0X) and with both bosons longitudinal (f_00), res

What carries the argument

The analysis hinges on three deep neural-network classifiers (Pol.X0, Pol.0X, Pol.00) that separate each polarisation state from all others, and on a signal-vs-background DNN that separates electroweak WZjj production from QCD-induced WZjj and other backgrounds. The two-dimensional plane of the signal-vs-background score and a polarisation DNN score is partitioned into ten Voronoi regions per measurement, whose event counts are fitted with a binned maximum-likelihood profile fit that also constrains top-quark and ZZ backgrounds in dedicated control regions. The polarisation fractions are defined in the diboson centre-of-mass frame, and the sum of all four joint-polarisation fractions is fixe

Load-bearing premise

The load-bearing premise is that the shapes and relative yields of the polarisation states that are not being measured follow the Monte Carlo prediction, with the sum of fractions fixed to one; if the true non-measured fractions deviate from the simulation, the fitted f_X0 would absorb the difference.

What would settle it

Repeating the same fit on pseudo-data generated with the non-measured polarisation fractions deliberately shifted by, say, ±0.1 from the SM values and checking whether the recovered f_X0 stays within a few percent of its input value; if it does not, the 4.0σ evidence could be an artifact of the fixed-template assumption. Alternatively, a full Run 3 real-data analysis returning f_X0 more than two standard deviations away from the SM value would contradict the paper's central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The measured f_X0 provides a direct, channel-specific test of the Standard Model's mechanism for electroweak symmetry breaking in the high-energy longitudinal-scattering regime; a future deviation would signal new physics affecting the Z boson's longitudinal coupling.
  • The 95% CL upper limits on f_0X and f_00 bound the possible presence of longitudinal W bosons and double-longitudinal events in WZjj-EW, complementing the evidence seen in same-sign WW scattering.
  • The demonstrated DNN-plus-Voronoi-region methodology is transferable to other vector-boson scattering channels, such as ZZjj-EW, where a similar or better sensitivity can be expected.
  • The measured 13.6 TeV fiducial cross-section, consistent with the generator prediction, adds a new data point for tuning electroweak production models.

Where Pith is reading between the lines

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

  • If the 4.0σ signal persists and the fraction stays aligned with the SM prediction as the full Run 3 dataset is analysed, the case for the Higgs mechanism as the agent that keeps longitudinally polarised gauge-boson scattering unitary will be strengthened; conversely, a mismatch would make WZjj-EW the most sensitive channel for anomalous triple-gauge couplings.
  • The analysis's reliance on MC-fixed proportions among the non-measured polarisation states could be dropped once more data arrive; fitting all four joint fractions simultaneously would test the SM prediction of their correlations rather than assume it.
  • A natural next step would be to measure the polarisation fractions differentially as a function of m_jj or the boson-pair invariant mass, where the longitudinal component is expected to grow, giving a sharper probe of the unitarity-cancellation mechanism.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The paper presents measurements of W and Z boson polarisation states in electroweak WZjj production using 140 fb^-1 of 13 TeV and 164 fb^-1 of 13.6 TeV pp collision data recorded by ATLAS. A profile-likelihood fit to DNN-based Voronoi regions in the signal region, together with control regions for ttV, tZj and ZZ backgrounds, is used to extract the fraction fX0 of WZjj-EW events with a longitudinally polarised Z boson, the fraction f0X with a longitudinally polarised W boson, and the double-longitudinal fraction f00. The measured fX0 = 0.324 ± 0.088 (stat. 0.086, syst. 0.017) yields an observed significance of 4.0 standard deviations (2.9 expected), in agreement with the NLO EW prediction of 0.2745 ± 0.0008. Upper limits are set on f0X and f00, and the fiducial WZjj-EW cross-section at 13.6 TeV is measured as 0.374 ± 0.077 (stat.) ± 0.053 (syst.) ± 0.009 (lumi.) fb.

Significance. If the result holds, this is the first evidence for longitudinally polarised Z bosons in electroweak WZjj production, a process directly sensitive to electroweak symmetry breaking and to the Higgs-sector cancellations in vector-boson scattering. The measurement is statistically dominated, uses a well-documented likelihood with control regions, and is compared with multiple independent SM predictions (MadGraph, Sherpa, MoCaNLO NLO EW). The agreement of fX0 with the SM NLO EW prediction, despite the observed significance exceeding the expectation, is an important consistency check. The cross-section measurement at 13.6 TeV is also a useful input for SM tests. The analysis is careful and the systematic treatment is detailed; the main caveat concerns the quantitative robustness of the fX0 extraction to the fixed relative composition of polarisation-state templates.

major comments (1)
  1. [Section 7, paragraph 'For the separate measurements...'] The fX0 fit uses templates for the 'measured' X0 state and the 'non-measured' XT state, each being a weighted sum of two joint polarisation states (X0 = W0Z0 + WTZ0; XT = W0ZT + WTZT), with the weights taken from the MC prediction. The text states that fits allowing the non-measured proportions to vary give consistent results and that pseudo-data closure tests with injected variations recover the true fX0, but no numerical results are given. Since the 4.0σ evidence claim is the central result and the total systematic uncertainty on fX0 is only 5.3%, an unquantified bias of order 0.04–0.05 in fX0 would materially change the significance. Please report the numerical bias and pull from the closure tests, including (if performed) variations of both the X0 and XT internal compositions, and the shift in fX0 when the non-measured proportions are allowed to float in data. If a non-negligible bia
minor comments (4)
  1. [Section 7] The sentence 'Fits to data allowing the respective proportions of non-measured polarisation states to vary were also tested and yield consistent results' would be more informative if it specified how the additional parameters were constrained (e.g., flat priors, Gaussian constraints) and whether this was done for all three fits (fX0, f0X, f00).
  2. [Section 8 / Table 3] The 'WZjj-EW Theory modelling' uncertainty on fX0 is reported as 1.7%, while the text describes shape variations of up to 20% in the Voronoi regions. Clarify how these shape variations translate into the 1.7% uncertainty on fX0, and whether the fixed non-measured fraction ratio is covered by this or by any other systematic.
  3. [Table 5] The f00 measurement is reported as 0.000 ± 0.134 with zero systematic uncertainty. A short note explaining that the fit is at the boundary (hence zero syst.) would avoid confusion.
  4. [Abstract / Section 9] The significance is quoted as 4.0σ without the corresponding p-value. For an evidence-level claim, reporting the p-value (or the one-sided significance definition) would be helpful, especially since the observed significance is higher than expected.

Circularity Check

0 steps flagged

No significant circularity: the measured polarisation fractions are free parameters fitted to data and compared with external SM predictions; fixed MC assumptions for non-measured states are a modelling choice, not an input-to-output equivalence.

full rationale

The central measurement, fX0, is a free parameter of a binned maximum-likelihood fit to data in the signal region, using templates for the four polarisation states from Sherpa3, MadGraph and MoCaNLO. The paper states: 'In each fit, the sum of the measured and non-measured polarisation fractions is enforced to be one... the respective proportions of polarisation states among the non-measured ones are taken from the MC prediction.' This is a fixed modelling assumption for nuisance/template composition, but it does not define the fitted fX0 in terms of itself. The paper explicitly reports robustness checks: 'Fits to data allowing the respective proportions of non-measured polarisation states to vary were also tested and yield consistent results. Fits to pseudo-data with injected variations of the non-measured polarisation fractions, deviating from the SM expectation, were performed. In all cases, the fits are able to recover the true measured polarisation fractions.' The final result is compared with independent predictions from MadGraph, Sherpa3.0 and NLO EW MoCaNLO calculations, so the SM prediction is not used as the measured value. The quoted WZjj-EW theory modelling uncertainty (1.7% on fX0) covers template-shape variations, and the fixed non-measured fractions are a documented conditional-modelling assumption rather than a circular construction. Self-citations to previous ATLAS measurements [8, 11, 12] supply established experimental methods, detector calibrations and earlier validated measurements; they are not unverified uniqueness theorems or ansätze that secretly impose the result. No step in the derivation chain reduces by construction to a fitted input or to a self-citation; the analysis is a standard data-driven template fit benchmarked against external theory.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The measurement depends on the SM/MC description of polarised-signal shapes and background templates, with the polarisation fractions themselves fitted from data. No new particles, forces or conserved quantities are introduced.

free parameters (6)
  • fX0 (longitudinal-Z fraction) = 0.324 ± 0.088 (total)
    Central measured quantity from the profile-likelihood fit to signal-region Voronoi regions.
  • f0X (longitudinal-W fraction) = 0.007 ± 0.151; 95% CL upper limit 0.19
    Fitted simultaneously; near-zero best fit against SM expectation 0.276.
  • f00 (double-longitudinal fraction) = 0.000 ± 0.134; 95% CL upper limit 0.12
    Fitted; consistent with zero and with SM expectation 0.090.
  • mu_WZjj-EW normalisation factor = 1.06 ± 0.18 (from fX0 fit)
    Common signal-strength parameter across Run 2 and Run 3, used to derive the fiducial cross-section.
  • WZjj-QCD renormalisation factor = 0.74 ± 0.06 (Run 2), 0.80 ± 0.05 (Run 3)
    Free nuisance normalisation constrained by signal-region data in the fit.
  • Background normalisations mu_ttV, mu_tZj, mu_ZZ = mu_ttV = 0.96 ± 0.12 (1.09 ± 0.14); mu_tZj = 1.18 ± 0.22 (1.15 ± 0.22); mu_ZZ = 1.09 ± 0.11 (0.97 ± 0.11), Run 2 (Run 3)
    Nuisance parameters constrained by the b-CR and ZZ-CR control regions.
axioms (5)
  • domain assumption Polarised on-shell WZjj-EW signal templates (Sherpa3 MEPS@LO, narrow-width approximation) describe detector-level DNN-score shapes.
    Section 4 simulation setup; NLO EW corrections are applied only as a shape uncertainty in Section 8.
  • domain assumption Non-measured polarisation fractions follow the SM/MC prediction in each of the three single-fraction fits.
    Section 7: 'the respective proportions of polarisation states among the non-measured ones are taken from the MC prediction.'
  • domain assumption Small interference (~2%) and off-shell (~1.5%) contributions are absorbed into effective polarisation fractions.
    Section 3, final paragraph, based on the MoCaNLO NLO EW estimate.
  • domain assumption The spin-density-matrix/fiducial polarisation definition with z-axis along the boson direction in the WZ rest frame is the appropriate observable.
    Section 3 establishes the reference frame citing Ref. [19].
  • domain assumption Background modelling for WZjj-QCD, ZZjj, ttV, tZj and misidentified leptons is correct within the assigned uncertainties.
    Section 6 and Section 8; normalisations are constrained via dedicated control regions.

pith-pipeline@v1.3.0-alltime-deepseek · 61093 in / 16655 out tokens · 131879 ms · 2026-08-01T10:21:41.886117+00:00 · methodology

0 comments
read the original abstract

Measurements of polarisation states of $W$ and $Z$ gauge bosons in electroweak $W^{\pm}Z$ production in association with two jets ($WZjj\mathrm{-EW}$) in proton-proton collisions are presented. The data set used corresponds to integrated luminosities of 140 fb$^{-1}$ and 164 fb$^{-1}$ of proton-proton collisions at centre-of-mass energies of 13 TeV and 13.6 TeV, respectively, recorded by the ATLAS detector at the CERN Large Hadron Collider. The $W^{\pm}Z$ candidate events are reconstructed using leptonic decay modes of the gauge bosons into electrons and muons. The observed significance for the presence in data of $WZjj\mathrm{-EW}$ events containing a longitudinally polarised $Z$ boson is of 4.0 standard deviations. The measured fraction of such events, integrated over the fiducial region, is $f_{\mathrm{X0}} = 0.32 \pm 0.09$, in agreement with the Standard Model prediction at next-to-leading-order in electroweak corrections. Upper limits at 95% confidence level of 0.19 and 0.12 are set on the fraction of events with a $W$ boson longitudinally polarised and on the fraction of events with the two bosons longitudinally polarised, respectively. The integrated fiducial cross-section per lepton flavour of $WZjj\mathrm{-EW}$ production at $\sqrt{s} = 13.6$ TeV is also measured to be $\sigma_{WZjj\mathrm{-EW} \rightarrow \ell^{'} \nu \ell \ell jj} = 0.374 \; \pm 0.077 (\mathrm{stat.}) \; \pm 0.053 (\mathrm{syst.}) \; \pm 0.009 (\mathrm{lumi.}) \; \mathrm{fb}$, where $\ell$ and $\ell^{'}$ are either an electron or a muon. This measurement is in agreement with the Standard Model expectation.

discussion (0)

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