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A test of $CP$ invariance in Higgs boson production via vector-boson fusionhas been performed in the $H\rightarrow\gamma\gamma$ channel using 139fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13\,\mathrm{TeV}$collected by the ATLAS detector at the LHC. The Optimal Observable method isused to probe the $CP$ structure of interactions between the Higgs boson andelectroweak gauge bosons, as described by an effective field theory. No sign of$CP$ violation is observed in data. Constraints are set on the parametersdescribing the strength of the $CP$-odd component in the coupling between theHiggs boson and the electroweak gauge bosons in two effective field theorybases: $\tilde{d}$ in the HISZ basis and $c_{H\tilde{W}}$ in the Warsaw basis.The results presented are the most stringent constraints on $CP$ violation inthe coupling between Higgs and weak bosons. The 95% CL constraint on$\tilde{d}$ is derived for the first time and the 95% CL constraint on$c_{H\tilde{W}}$ has been improved by a factor of 5 compared to the previousmeasurement.

Study of the $CP$ property of the Higgs boson to electroweak boson coupling in the VBF $H\to\gamma\gamma$ channel with the ATLAS detector