The Higgs boson as a probe for new physics: Investigation of CP properties and search for associated dark matter production with ATLAS Run 2 data

This thesis presents studies of the Higgs boson using the full Run 2 proton-proton collision dataset collected by the ATLAS experiment at the LHC at a centre-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$. The CP properties of the Higgs boson are investigated in the vector-boson fusion production mode, using its decay into $\tau$-leptons. To probe potential CP-violating interactions between the Higgs boson and electroweak gauge bosons, the Optimal Observable method is employed in the framework of effective field theory. No significant deviations from the Standard Model are observed, and constraints are placed on CP-odd parameters, interpreted both in the HISZ basis via $\tilde{d}$ and in the Warsaw basis via the Wilson coefficient $c_{H\tilde{W}}$. The stand-alone result from the fully leptonic channel yields a 95% confidence interval of $\tilde{d}\in[-0.078,\, 0.091]$ and $c_{H\tilde{W}} \in[-1.38,\, 1.71]$. Further enhancement is obtained by statistically combining all three decay modes of the $\tau$-lepton pair, with combined measurements of $\tilde{d} \in [-0.012,\, 0.049]$ and $c_{H\tilde{W}} \in [-0.24,\, 0.84]$ at 95% confidence level. The latter represents one of the strongest limits on the $c_{H\tilde{W}}$ Wilson coefficient to date.

Additionally, dark matter production in association with a Higgs boson decaying into hadronically decaying $\tau$-leptons is investigated, using the same dataset. No evidence of new physics is observed, and the results are interpreted in the context of a two-Higgs-doublet model with an additional pseudoscalar mediator (2HDM+$a$), with exclusion limits set at 95% confidence level on the model parameters. Model-independent upper limits on the visible cross-section of new physics in the $E_{\textrm{T}}^{\textrm{miss}}+h(\tau\tau)$ final state are also computed, ranging from 0.04 to 0.08 fb depending on the signal region.