Probing the $\mathcal{CP}$ nature of the Higgs boson coupling to $\tau$ leptons at HL-LHC

This note presents a study for the prospective measurement of the $\mathcal{CP}$ quantum number of the Higgs boson coupling to $\tau$ leptons with 3000 fb$^{-1}$ of proton--proton collisions at $\sqrt{s} = 14$ TeV using the ATLAS detector at the HL-LHC. Only $H\to\tau\tau$ events where both $\tau$ leptons decay via the $\tau ^{\pm} \rightarrow \rho ^{\pm} \nu _{\tau} \rightarrow \pi^{0} \pi^{\pm} \nu _{\tau}$ chain are analysed and the acoplanarity angle $\varphi ^*_{\mathcal{CP}}$, the angle between the planes spanned by the pion pairs, is used to determine the $\mathcal{CP}$-mixing angle. It is shown that considering only statistical uncertainties, a pseudoscalar Higgs boson can be excluded at 95% confidence level. The $\mathcal{CP}$-mixing angle can be measured with a statistical precision ranging between $\pm18^{\circ}$ and $\pm33^{\circ}$, depending on the precision of the $\pi^0$ reconstruction.