Measurement of the $CP$ properties of Higgs boson interactions with $\tau$-leptons with the ATLAS detector

A study of the charge conjugation and parity ($CP$) properties of the interaction between the Higgs boson and $\tau$-leptons is presented. The study is based on a measurement of $CP$-sensitive angular observables defined by the visible decay products of $\tau$-lepton decays, where at least one hadronic decay is required. The analysis uses 139 fb${}^{-1}$ of proton$-$proton collision data recorded at a centre-of-mass energy of $\sqrt{s}=13$ TeV with the ATLAS detector at the Large Hadron Collider. Contributions from $CP$-violating interactions between the Higgs boson and $\tau$-leptons are described by a single mixing angle parameter ${\phi }_{\tau }$ in the generalised Yukawa interaction. Without assuming the Standard Model hypothesis for the $H\to \tau \tau$ signal strength, the mixing angle ${\phi }_{\tau }$ is measured to be $9^{\circ }\pm {16}^{\circ }$, with an expected value of $0^{\circ }\pm {28}^{\circ }$ at the 68% confidence level. The pure $CP$-odd hypothesis is disfavoured at a level of 3.4 standard deviations. The results are compatible with the predictions for the Higgs boson in the Standard Model.