A test of CP invariance in Higgs boson production via vector-boson fusion using the method of the Optimal Observable is presented. The analysis exploits the decay mode of the Higgs boson into a pair of $\tau$ leptons and is based on 20.3 fb$^{-1}$ of proton—proton collision data at $\sqrt{s}$ = 8 TeV collected by the ATLAS experiment at the LHC. Contributions from CP-violating interactions between the Higgs boson and electroweak gauge bosons are described in an effective field theory framework, in which the strength of CP violation is governed by a single parameter $\tilde{d}$. The mean values and distributions of CP-odd observables agree with the expectation in the Standard Model and show no sign of CP violation. The CP-mixing parameter $\tilde{d}$ is constrained to the interval [-0.11,0.05] at 68% confidence level, consistent with the Standard Model expectation of $\tilde{d}=0$.

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