Analysis of the $Wtb$ vertex from the measurement of triple differential angular decay rates of single top quarks produced in the $t$-channel at $\sqrt{s}=$8 TeV with ATLAS detector

The electroweak production and subsequent decay of single top quarks is determined by the properties of the $Wtb$ vertex, which can be described by the complex parameters of an effective Lagrangian. An analysis of angular distributions of the decay products of single top quarks produced in the $t$-channel constrains these parameters simultaneously. The thesis presents an analysis using 20.2 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of 8 TeV collected with the ATLAS detector at the LHC. The fraction $f_1$ of decays containing transversely polarised $W$ bosons is measured to be $f_1=0.296^{+0.048}_{-0.051}$ (stat. + syst.). The phase $\delta_-$ between amplitudes for transversely and longitudinally polarised $W$ bosons recoiling against left-handed $b$-quarks, is measured to be $\delta_- = 0.002\pi^{+0.016\pi}_{-0.017\pi}$ (stat. + syst.), giving no indication of $CP$ violation. The fraction of longitudinal to transverse $W$ bosons accompanied by right-handed $b$-quarks are also constrained at 95% C.L. to $f_1^+ < 0.118$ and $f_0^+ < 0.085$. Based on these measurements limits are placed at 95% C.L. on the ratio of the complex coupling parameters $g_\mathrm{R}$ and $V_\mathrm{L}$ such that Re$[g_\mathrm{R}/V_\mathrm{L}] \in [-0.122,0.168]$ and Im$[g_\mathrm{R}/V_\mathrm{L}] \in [-0.066,0.059]$. Constraints are also placed on the magnitudes of the ratios $|V_\mathrm{R}/V_\mathrm{L}|$, and $|g_\mathrm{L}/V_\mathrm{L}|$. Finally the polarisation of single top quarks in the $t$-channel is constrained to be $P > 0.718$ (95% C.L.). None of the above measurements make assumptions on the value of any of the other parameters or couplings and all of them are in agreement with the Standard Model.