Measurement of the $W$ boson helicity fractions in $t\bar{t}$ events at $\sqrt s=$ 8 TeV in the lepton+jets channel with the ATLAS detector

Precise measurements of the properties of the top quark allow for testing the Standard Model (SM) and can be used to constrain new physics models. The top quark is predicted in the SM to decay almost exclusively to a $W$ boson and $b$-quark. Thus, studying the $Wtb$ vertex structure at high precision and in detail is motivated. This thesis presents a measurement of the $W$ boson helicity fractions in top quark decays with $t\bar{t}$ events in the lepton + jets final state using proton-proton collisions at a centre-of-mass energy of $\sqrt s$ = 8 TeV recorded in 2012 with the ATLAS detector at the LHC. The data sample corresponds to an integrated luminosity of 20.2~fb$^{-1}$. The angular distribution of two different analysers, the charged lepton and the down-type quark in the $W$ boson rest frame are used to measure the helicity fractions. The most precise measurement is obtained from the leptonic analyser and events which contain at least two $b$-quark tagged jets. The results of $F_{0}$ = 0.709 $\pm$ 0.012 (stat.+bkg. norm.) ${}^{+0.015}_{-0.014}$ (syst.), $F_{L}$ = 0.299 $\pm$ 0.008 (stat.+bkg. norm.) ${}^{+0.013}_{-0.012}$ (syst.), $F_{R}$ = -0.008 $\pm$ 0.006 (stat.+bkg. norm.) $\pm$ 0.012 (syst.) which stand for longitudinal, left- and right-handed $W$ boson helicity fractions respectively, are obtained by performing a combined fit of electron+jets and muon+jets channels to data. The measured helicity fractions are consistent with the Standard Model prediction. As the polarisation state of the $W$ boson in top quark decays is sensitive to the $Wtb$ vertex structure, limits on anomalous $Wtb$ couplings are set.