A Cross Section Measurement Of Events With Two Muons At The $Z^{0}$ Resonance And At Least One Heavy Flavour Jet At The Atlas Experiment Of The Large Hadron Collider

In 2010, the Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) near Geneva (Switzerland) came into full operation providing proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = \unit[7]{TeV}$. LHC data may allow the observation of the Higgs boson, the last unknown building block of the standard model of particle physics (SM). Di-muon final states containing heavy flavour jets pose an irreducible background for searches of the Higgs boson as predicted the SM or theories beyond. They also provide a unique testbed for tests of perturbative Quantum Chromo-Dynamics (pQCD). This thesis provides a measurement of the cross section of events with one di-muon pair with an invariant mass in the $Z^0$ mass region and at least one heavy flavour jet. Studies on acceptance and systematic effects of the experimental setup are presented as well as a comparison to theoretical predictions. The total inclusive cross section of $Z^{0}+b$ events was observed as $\sigma(\mu^{+}\mu^{-}+b+X) = \unit[(4.15 ^{+0.97}_{-0.89} (stat.) ^{+0.45}_{-0.53} (syst.))]{pb} $ from the equivalent of $\unit[36]{pb^{-1}}$ of data. Agreement with pQCD predictions at next-to leading order (NLO) is found while tensions with leading order (LO) predictions are observed. Further, the cross-section ratio $\mathcal{R} = \frac{\sigma_{incl}(Z^{0}+b)}{\sigma_{incl}(Z^{0}+\text{jets})}$ with events containing two muons and at least one jet of any origin was measured to $\mathcal{R} = \unit[4.6 ^{+1.4}_{-1.2} (stat.) \pm 0.5 (syst.)]{\%}$. This is found to agree with NLO and LO calculations within known uncertainties.