A longitudinal view on symmetry breaking

The Brout–Englert–Higgs (BEH) mechanism, the cornerstone of electroweak symmetry breaking, gives the W and Z bosons their masses. With them comes a longitudinal polarisation, which sets the weak bosons apart from photons and other massless particles, thus providing a direct probe of the BEH mechanism. The ATLAS collaboration has now studied this longitudinal mode in two analyses of di-boson events, providing new insight into rare electroweak processes. The results are based on proton-proton collision data from the full Run 2, with 140 fb^–1 at 13 TeV, and from part of Run 3, with 164 fb^–1 at 13.6 TeV.

The first result targets the rare production of two Z bosons, selecting events where both decay into electron or muon pairs. Since the leptons’ angular distributions reflect the parent bosons’ polarisation, researchers trained a multivariate classifier on these observables to distinguish events containing two longitudinally polarised Z bosons from those with other polarisation combinations. The combined Run 2 and Run 3 analysis achieved a 6.5σ observed significance (5.6σ expected), marking the first observation of this rare process (see figure 1). The team also measured the Z-boson polarisation fractions for the full dataset and in different ranges of the four-lepton invariant mass. The measured results agree well with the Standard Model (SM), which predicts such events to become increasingly rare at higher energies.

The second result concerns polarisation in WZ diboson events with leptonic decays to electrons and muons, produced in association with two hadronic jets. The phase space is enriched in electroweak WZjj production, which includes processes where the two vector bosons scatter off one another. The scattering of two longitudinally polarised bosons can occur via Higgs-boson exchange, which prevents the SM calculations for this process from diverging at high energies. If the Higgs boson deviated from the SM prediction, new physics – such as new resonances – would be necessary to restore physical behaviour. This makes the study highly sensitive to new physics in the electroweak sector.

The experimental challenge lies in the rarity of the electroweak production process. Even after a dedicated selection, only 13% of the resulting events are predicted to stem from it. To address this, researchers used a two-dimensional plane with axes representing a signal-versus-background discriminator and a polarisation discriminator, both derived via a deep neural network. A maximum-likelihood fit extracted the integrated electroweak WZjj cross section in the fiducial phase space. It also measured the fractions of longitudinal W and Z polarisations, each independently of the polarisation of the other boson in the pair, and the double longitudinal diboson polarisation fractions.

ATLAS found evidence for longitudinally polarised Z bosons with an observed (expected) significance of 4.0 (2.9) standard deviations, and an observed (expected) longitudinal Z-polarisation fraction of (32 ± 9)% ((27.45 ± 0.08)%) (see figure 2). The measured electroweak WZjj cross section agrees with predictions. No evidence was found for longitudinally polarised W bosons, regardless of the Z-boson polarisation, and upper limits were set on these fractions. All measurements remain consistent with SM predictions within 2.4 standard deviations.

Both analyses benefited from a collaboration with theorists to obtain predictions at next-to-leading order in the electroweak coupling, using the MoCaNLO framework. With more data from Run 3 and beyond, future analyses will sharpen tests of the BEH mechanism, improve sensitivity to potential deviations, and further expand the frontier of weak-boson polarisation physics.