Z boson and associated jet production at the LHCb experiment

The LHCb experiment at the Large Hadron Collider (LHC) is a fully instrumented forward-arm spectrometer initially designed to study the decays of heavy flavour particles produced close to the beam-line ($2.0<\eta<4.5$). This unique precision coverage of the forward region at the LHC means that the experiment is also able to make measurements of massive electroweak vector boson production which are complementary to those made at the general purpose detectors. Such measurements are sensitive to the inner structure of the proton, probing parton distribution functions at low values of Bjorken-$x$. These measurements also provide precision tests of perturbative quantum chromodynamics and the Standard Model. This thesis considers the production of Z bosons in association with jets at LHCb in events where the Z bosons decay directly to two muons. Jet reconstruction at LHCb makes use of a particle flow algorithm which enables the majority of the jet content to be measured using the LHCb tracking systems. This algorithm enables jets to be reconstructed with a transverse momentum resolution of about 11-13%. The measurement of the $Z+$jet production cross-section is made above two jet transverse momentum thresholds: 10 and 20 GeV, using data collected by the LHCb experiment in 2011 corresponding to an integrated luminosity of about 1 fb$^{-1}$. The fiducial region for these measurements is defined by requiring that both the Z boson and the jet lie within the LHCb detector's acceptance. Measurements are also made of the ratio of these cross-sections to the inclusive Z boson production cross-section, and of the differential cross-sections with respect to kinematic variables associated with the $Z+$jet events. These results show good agreement with theoretical predictions based on the Standard Model, evaluated by matching fixed order calculations using POWHEG to PYTHIA for simulation of the parton shower development and hadronisation. The thesis concludes by considering the impact of related future measurements.