Pinpointing polarisation in vector-boson scattering

In the Standard Model (SM), W and Z bosons acquire mass and longitudinal polarisation through electroweak (EW) symmetry breaking, where the Brout–Englert–Higgs mechanism transforms Goldstone bosons into their longitudinal components. One of the most powerful ways to probe this mechanism is through vector-boson scattering (VBS), a rare process represented in figure 1, where two vector bosons scatter off each other. At high (TeV-scale) energies, interactions involving longitudinally polarised W and Z bosons provide a stringent test of the SM. Without the Higgs boson’s couplings to these polarisation states, their interaction rates would grow uncontrollably with energy, eventually violating unitarity, indicating a complete breakdown of the SM.

Measuring the polarisation of same electric charge (same sign) W-boson pairs in VBS directly tests the predicted EW interactions at high energies through precision measurements. Furthermore, beyond-the-SM scenarios predict modifications to VBS, some affecting specific polarisation states, rendering such measurements valuable avenues for uncovering new physics.

Using the full proton–proton collision dataset from LHC Run 2 (2015–2018, 140 fb^–1 at 13 TeV), the ATLAS collaboration recently published the first evidence for longitudinally polarised W bosons in the electroweak production of same-sign W-boson pairs in final states including two same-sign leptons (electrons or muons) and missing transverse momentum, along with two jets (EW W^±W^±jj). This process is categorised by the polarisation states of the W bosons: fully longitudinal (W_L^±W_L^±jj), mixed (W_L^±W_T^±jj), and fully transverse (W_T^±W_T^±jj). Measuring the polarisation states is particularly challenging due to the rarity of the VBS events, the presence of two undetected neutrinos, and the absence of a single kinematic variable that efficiently distinguishes between polarisation states. To overcome this, deep neural networks (DNNs) were trained to exploit the complex correlations between event kinematic variables that characterise different polarisations. This approach enabled the separation of the fully longitudinal W_L^±W_L^±jj from the combined W_T^±W^±jj (W_L^±W_T^±jj plus W_T^±W_T^±jj) processes as well as the combined W_L^±W^±jj (W_L^±W_L^±jj plus W_L^±W_T^±jj) from the purely transverse W_T^±W_T^±jj contribution.

To measure the production of W_L^±W_L^±jj and W_L^±W^±jj processes, a first DNN (inclusive DNN) was trained to distinguish EW W^±W^±jj events from background processes. Variables such as the invariant mass of the two highest-energy jets provide strong discrimination for this classification. In addition, two independent DNNs (signal DNNs) were trained to extract polarisation information, separating either W_L^±W_L^±jj from W_T^±W^±jj or W_L^±W^±jj from W_T^±W_T^±jj, respectively. Angular variables, such as the azimuthal angle difference between the leading leptons and the pseudorapidity difference between the leading and subleading jets, are particularly sensitive to the scattering angles of the W bosons, enhancing the separation power of the signal DNNs. Each DNN is trained using up to 20 kinematic variables, leveraging correlations among them to improve sensitivity.

The signal DNN distributions, within each inclusive DNN region, were used to extract the W_L^±W_L^±jj and W_L^±W^±jj polarisation fractions through two independent maximum-likelihood fits. The excellent separation between the W_L^±W^±jj and W_T^±W_T^±jj processes can be seen in figure 2 for the W_L^±W^±jj fit, achieving better separation for higher scores of the signal DNN, represented in the x-axis. An observed (expected) significance of 3.3 (4.0) standard deviations was obtained for W_L^±W^±jj, providing the first evidence of same-sign WW production with at least one of the W bosons longitudinally polarised. No significant excess of events consistent with W_L^±W_L^±jj production was observed, leading to the most stringent 95% confidence-level upper limits to date on the W_L^±W_L^±jj cross section: 0.45 (0.70) fb observed (expected).

There is still much to understand about the electroweak sector of the Standard Model, and the measurement presented in this article remains limited by the size of the available data sample. The techniques developed in this analysis open new avenues for studying W- and Z-boson polarisation in VBS processes during the LHC Run 3 and beyond.