Tau identification algorithms and study of the CP structure of the Yukawa coupling between the Higgs boson and tau leptons in CMS

<!--HTML-->The measurement of the CP properties of the Yukawa coupling of the Higgs boson to $\tau$ leptons is presented. The data set used for the analysis is collected by the CMS experiment at the LHC during the Run 2 data-taking period in proton-proton collisions at $\sqrt{S}$ = 13 TeV and corresponds to an integrated luminosity of 137 fb$^{-1}$ . The Yukawa coupling between the Higgs boson and $\tau$ leptons is parametrised in terms of the effective mixing angle $\alpha$$^{H}$$^{\tau}$$^{\tau}$, where the value $\alpha$$^{H}$$^{\tau}$$^{\tau}$ = 0$^{\circ}$(90$^{\circ}$) corresponds to the SM scenario of the pure CP-even (CP-odd) H$\tau$$\tau$ coupling.<br>The angle between the decay planes of the $\tau$ leptons is used as the observable encoding the CP nature of the Higgs boson. The measurement is performed in the $\tau$$_{e}$$\tau$$_{h}$ channel where one $\tau$ lepton decays into an electron and the other hadronically. The results are combined with the measurement in the $\tau$$_{\mu}$$\tau$$_{h}$ and $\tau$$_{h}$$\tau$$_{h}$ channels. The observed (expected) value of the effective mixing angle for the combination is measured to be: $\alpha$$^{H}$$^{\tau\tau}$ = -1 $\pm$ 19$^{\circ}$ (0 $\pm$ 21$^{\circ}$) @68.3% CL.<br>The results are compatible with the SM expectation and the pure CP-odd hypothesis is rejected at the observed (expected) significance level of 3.0 (2.6) standard deviations.<br>The improvements to the $\tau$ lepton identification in CMS in the context of the Run 3 preparation are described. Retraining and optimisation of the DeepTau algorithm with the addition of the adversarial fine-tuning procedure are performed. The resulting model improves upon the previous DeepTau model in terms of the background rejection by 10-50% and has a better description of data with simulation in the H → $\tau$$\tau$ selection region.<br>A new algorithm called Tau Transformer (TaT) is proposed to overcome the limitations of the DeepTau architecture. The TaT core is based on self-attention layers and features the embedding module allowing for the multimodality treatment of the input representation. Comparison of the TaT model with the retrained DeepTau model and a comparable ParticleNet-based architecture shows consistently improved performance by up to 50% in the misidentification rate across the $p$$_{T}$, $\eta$, and decay mode ranges of interest.