A measurement of $\sigma \left( Z \rightarrow \mu \mu \right)$ using the LHCb detector at CERN

LHCb is one of four main experiments at the LHC in CERN. This thesis analyses 1.03 fb$^{-1}$ of $\sqrt{s} = 7$ TeV data collected in 2011. Measurements of the $Z\rightarrow\mu\mu$ cross-section and a differential measurement with respect to $Z$ boson rapidity are presented. The primary motivations for making these measurements are to probe the accuracy of the Standard Model and constrain theoretical parton distribution functions. Final state radiation causes a downward shift in the reconstructed dimuon invariant mass and broadening in the peak. Reconstructing the radiated photon means the invariant mass distribution shift can be corrected for. Here final state radiation is implemented in LHCb simulation for the first time. It is used to study the effect on the reconstructed $Z$ mass distribution. Selections are placed on the distance between the photon and muon, and the photon $P_T$. The distribution is fitted to be 12% narrower than the non-reconstructed sample. The measured mass of the $Z$ boson is increased from 91.047 GeV to 91.054 GeV. The kinematic requirements placed on the muons are: both muons must have transverse momentum, $P_T > 20$ GeV; the dimuon invariant mass, $60 < M_{\mu\mu} < 120$ GeV; and their pseudorapidity, $2 < \eta_{\mu} < 4.5$. These selections are justified using simulation. Once the event requirements are imposed 56449 $Z$ boson candidates are yielded. Background contamination is estimated using data driven methods where possible, and simulation. The number of background events in the signal region is estimated to be $254.9 \pm 7.0$. The signal efficiency is determined by analysing each source individually. The overall efficiency for measuring a $Z\rightarrow\mu\mu$ event is found to be $0.74 \pm 0.02$. Taking these results into consideration the cross-section is measured to be: \begin{eqnarray} &\sigma_{Z\rightarrow\mu\mu} \left( 2<\eta_{\mu}<4.5,\; P_{T}^\mu > 20 \; \mathrm{GeV}, \; 60 < M_{\mu\mu} < 120 \; \mathrm{GeV} \right) = \nonumber\\ &\bigl( 74.2 \;\pm 0.4\; (\mathrm{stat})\; \pm 2.0\; (\mathrm{sys})\; \pm 2.6\; (\mathrm{lumi}) \bigr)\; \mathrm{pb} \nonumber \end{eqnarray} A comparison with NLO theory predictions using CTEQ6.6 and MSTW2008 PDF sets is performed, and the above result is found to be consistent.