Measurement of the CP properties of the Higgs boson in its decays to $\tau$ leptons with the CMS experiment

The discovery of the Higgs boson in 2012 by the CMS and ATLAS collaborations marked the start of the exploration of the Higgs sector of particle physics. This thesis explores one of these measurements: the study of the CP properties of the Yukawa coupling between the Higgs and the $\tau$ lepton. The study discussed in this thesis is performed using data collected in proton-proton collisions at 13 TeV by the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC). The dataset used in the measurement was collected throughout the Run 2 data-taking period at the LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$. In $H$ $\rightarrow$ $\tau$$\tau$ decays the amount of CP-mixing in the Yukawa coupling can be expressed in terms of the CP mixing $\varphi$$_{\tau}$$_{\tau}$, defined such that $\varphi$$_{\tau}$$_{\tau}$ = 0, $\pi$/2 and $\pi$/4 correspond to a pure CP-even, CP-odd and maximal CP-mixing cases. This angle can be inferred by measuring the angle between the decay planes of the two $\tau$ leptons ($\varphi$$_{CP}$ ). The decay planes reconstruction was performed using dedicated methods for each decay channel. The estimation of most background processes was performed using data-driven methods, while a neural network was used to identify Higgs decays with respect to the dominant backgrounds. The measurement was performed in this thesis in the final state where a tau lepton decays muonically and the other one hadronically ($\tau$$_{\mu}$$\tau$$_{h}$), and combined with one performed in the fully hadronic final state ($\tau$$_{h}$$\tau$$_{h}$). The measured CP admixture is $\varphi$$_{\tau}$$_{\tau}$ = (4 $\pm$ 17)$^{o}$ [(0±23)$^{◦}$], corresponding to a significance for the exclusion of a pure CP-odd hypothesis of 3.2$\sigma$ (2.3$\sigma$). The results are in good agreement with the SM prediction of a pure CP-even coupling, and allow to exclude at 95% confidence level models that predict CP-even and CP-odd Yukawa couplings of comparable magnitude.