A precise measurement of the Z boson cross-section and a test of the Standard Model using the LHCb detector

Measurements of production cross-sections for $Z$ bosons that decay to muons are presented in this thesis. The data used to perform the measurements were recorded by the LHCb detector during $pp$ collisions at centre-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of approximately 1.0 and 2.0 fb$^{-1}$. The cross-sections are measured for muons in the pseudorapidity range $2.0 <\eta < 4.5$ with transverse momenta $p_{T} > 20$ GeV/c. The dimuon mass is restricted to $60 < M_{\mu^{+}\mu^{-}} < 120$ GeV/c$^{2}$. Total cross-sections are determined with a precision of approximately 2$\%$. Cross-sections are also measured as functions of kinematic variables relating to the $Z$ boson. Ratios of production cross-sections of electroweak bosons are presented using measurements of $W$ boson production. A precise test of the Standard Model is provided by the measurement of the ratio $$\frac{\sigma_{W^{+}\rightarrow\mu^{+}\nu_{\mu}} + \sigma_{W^{-}\rightarrow\mu^{-}\bar{\nu}_{\mu}}}{\sigma_{Z\rightarrow\mu^{+}\mu^{-}}} $$ where the uncertainty due to luminosity, and other correlated uncertainties, cancels. This cancellation allows the cross-section ratios to be measured with an overall precision below 1$\%$. Measurements of electroweak boson cross-section ratios as functions of muon $\eta$ are presented for the first time. Measurements of cross-section ratios and ratios-of-ratios of cross-sections at different centre-of-mass energies are also presented for the first time. Cross-section ratios at different centre-of-mass energies are determined with a precision of approximately 1.6$\%$. Ratios-of-ratios of cross-sections are measured with an overall precision below 1$\%$. All measurements are consistent with the predictions of the SM. It is expected that the data presented here will help place significant constraints on the form of proton PDFs.