Test of $CP$ Invariance in Higgs Boson Vector-Boson-Fusion Production Using the $H\to \gamma \gamma $ Channel with the ATLAS Detector

A test of $CP$ invariance in Higgs boson production via vector-boson fusion has been performed in the $H\to \gamma \gamma $ channel using $139\text{}\text{}{\mathrm{fb}}^{-1}$ of proton-proton collision data at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ collected by the ATLAS detector at the LHC. The optimal observable method is used to probe the $CP$ structure of interactions between the Higgs boson and electroweak gauge bosons, as described by an effective field theory. No sign of $CP$ violation is observed in the data. Constraints are set on the parameters describing the strength of the $CP$-odd component in the coupling between the Higgs boson and the electroweak gauge bosons in two effective field theory bases: $\stackrel{˜}{d}$ in the HISZ basis and ${c}_{H\stackrel{˜}{W}}$ in the Warsaw basis. The results presented are the most stringent constraints on $CP$ violation in the coupling between Higgs and weak bosons. The 95% C.L. constraint on $\stackrel{˜}{d}$ is derived for the first time and the 95% C.L. constraint on ${c}_{H\stackrel{˜}{W}}$ has been improved by a factor of 5 compared to the previous measurement.