Probing Higgs Boson physics in decays to tau leptons with the ATLAS experiment

The discovery of the Higgs boson in 2012 has opened up a new sector of particle physics to measurements of yet undiscovered couplings. Measurements of the numerous couplings of the Higgs boson - primarily through studies of bosonic decays - have consistently confirmed the Standard Model of Particle Physics. The measurement of fermionic Yukawa couplings, which is a free parameter of the Standard Model, is a critical test of the origin of mass in the Standard Model and serves as a probe for a wide array of new physics models. This thesis presents a measurement, search and feasibility study of couplings of the Higgs boson to the third generation lepton, the tau . A measurement is presented of the H -> tau tau cross-section which is performed using 36.1 inverse fb of sqrt(s) = 13 TeV collision data collected at the Large Hadron Collider by the ATLAS detector. A 6.4 sigma excess over the background-only hypothesis was observed in combination with sqrt(s) = 7, 8 TeV which constitutes a discovery of the final remaining coupling to third generation fermions. The total cross-section was measured as 3.70 +- 0.58(stat) +0.89-0.75(syst) pb, consistent with the expectation from the Standard Model. Several new physics models predict phenomena which can probed in supressed Higgs boson decays: one such phenomena is lepton flavour violation. A search for lepton flavour violating Higgs boson decays to e,mu and mu,e final states, using a new multivariate approach, is also detailed. This search used the same dataset as for the H -> tau tau cross-section. No excess is observed and upper limits on the branching ratio for H -> mu tau and H -> e tau of 0.47% and 0.28% are set, respectively. The limit on H -> e tau is now the new global limit. Finally a feasibility study for measuring the state of the Higgs boson using decays to two tau leptons is demonstrated. At tree-level, the H -> tau tau decays are sensitive to CP admixture couplings to a Higgs boson. One of the promising decay channel