Determination of the Relative Sign of the Higgs Boson Couplings to $W$ and $Z$ Bosons Using $WH$ Production via Vector-Boson Fusion with the ATLAS Detector

The associated production of Higgs and $W$ bosons via vector-boson fusion is highly sensitive to the relative sign of the Higgs boson couplings to $W$ and $Z$ bosons. In this Letter, two searches for this process are presented, using $140\text{}\text{}{\mathrm{fb}}^{-1}$ of proton-proton collision data at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ recorded by the ATLAS detector at the LHC. The first search targets scenarios with opposite-sign couplings of the $W$ and $Z$ bosons to the Higgs boson, while the second targets standard model-like scenarios with same-sign couplings. Both analyses consider Higgs boson decays into a pair of $b$ quarks and $W$ boson decays with an electron or muon. The data exclude the opposite-sign coupling hypothesis with a significance beyond $5\sigma $, and the observed (expected) upper limit set on the cross section for vector-boson fusion $WH$ production is 9.0 (8.7) times the standard model value at 95% confidence level.