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 (VBF) 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 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 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 decays into a pair of $b$-quarks and $W$ decays with an electron or muon. The opposite-sign coupling hypothesis is excluded with significance much greater than $5\sigma$, and the observed (expected) upper limit set on the cross-section for VBF $WH$ production is 9.0 (8.7) times the Standard Model value.