Measurement of the Drell--Yan triple-differential cross-section in $pp$ collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS detector

This thesis presents the measurement and results of the $Z/\gamma^{*}\rightarrow\mu^+\mu^-$ Drell--Yan triple-differential cross-section, using $20.24\,\mathrm{fb^{-1}}$ of ATLAS data recorded in 2012 at a centre-of-mass energy of $\sqrt{s}=8\,\mathrm{TeV}$. The triple-differential cross-section is measured as a function of dimuon invariant mass, $m_{\mu\mu}$, dimuon rapidity, $y_{\mu\mu}$, and lepton decay angle in the Collins-Soper frame, $\cos\theta^{*}$. These dimensions provide sensitivity to the parton composition of the proton through the parton density functions, PDFs, and the weak effective mixing angle, $\sin^2\theta^{\mathrm{eff.}}_{W}$, via the forward-backward asymmetry, $A_{FB}$. The measurement is performed on and around the Z-boson's invariant mass peak, $46< m_{\mu\mu}<200\,\mathrm{GeV}$, in a kinematic fiducial volume of muon transverse momentum, $p_{T}>20\mathrm{~GeV}$, and muon pseudo-rapidity $|\eta|\leq2.4$. The results are unfolded from the detector level to the Born, bare and dressed levels, where a precision of $<0.6\%$ is reported in the central bins. The data is combined with an electron channel measurement resulting in a combined result with reduced total uncertainty. The combined result is shown to constrain PDF uncertainties and achieve the most constrained $\sin^2\theta^{\mathrm{eff.}}_{W}$ uncertainty yet reported at the LHC.