Tau lepton universality test in the vector boson fusion topology using the ATLAS detector at the LHC

This thesis presents a lepton universality test using the data collected by the ATLAS experiment in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}$ = 13 TeV and an integrated luminosity of 139fb$^{-1}$. We probe the production of di-leptons across all lepton families in the vector boson fusion (VBF) topology. First, at di-lepton invariant masses around the Z pole, we derive a correction for the simulation of the production of lepton pairs coming from Z decays in association with jets initiated by QCD radiation (QCDjj) - this is the main background for the VBF production mode, where the two jets are coming from pure electroweak interactions (EWjj). We derive the corrections in the $Z$ $ll$ ($l=e,\mu$) final states and use them as input to correct the $Z\to\tau\tau$ final states. At the Z pole, we compute ratios between the EWjj signal strengths for the $e$-$\mu$ and $l$-$\tau$ final states ($l=e+\mu$); our results are $R_{e\mu} = 1.050 \pm 7.4\% (\text{Stat.}) \pm 2.9\% (\text{Syst.}) $ and $ R_{l\tau} = 1.092 \pm 18.5\% (\text{Stat.}) \pm 6.8\% (\text{Syst.})$, respectively. These results are consistent with the lepton universality hypothesis. The measurement uncertainties are dominated by the number of events collected by the ATLAS detector. Additionally, we present partially unblinded data-to-MC comparisons for events that have a high-invariant mass. The motivation is to look for hypothetical heavy resonances that only couple to the third generation of fermions and the W boson; if this is the case, they would be produced in the VBF mode. In the high-mass region, we discuss an unblinded Higgs control region - containing events with 116 $\leq$ $m$($\tau$$_{had}$$\tau$$_{lep}$)< 160 GeV; and a partially unblinded region including events with a higher di-lepton invariant mass than the Higgs region. Furthermore, this work includes a measurement of the performance of the tau identification (tauID) algorithm for high-$p$$_{T}$ using an alternative approach to the usual ATLAS tag-and-probe method in $t\bar{t}$ events. From the physics perspective our approach offers the advantage of being safer from lepton universality violation effects because our tau sample is populated from boosted Z boson decays. We measure data-to-MC ratios after applying the tauID criterion and then compute ratios between the $Z\to\tau\tau$ and $Z\to\iota\iota$ final states. This results in the partial cancellation of experimental systematics coming from the calibration of physics objects common to the light-lepton and tau final states; additionally, modelling and luminosity uncertainties are also reduced in the double ratio approach. The results have an uncertainty of $\approx$ 4% for 1-prong and $\approx$ 5% for 3-prong taus.