Central Exclusive Production of $\chi$ Mesons at LHCb

The LHCb experiment is a forward spectrometer at the Large Hadron Collider, covering a range of pseudorapidity $1.9<\eta<4.9$. It has a very precise vertex detector called the VELO, near the interaction point. The monitoring software for the VELO is discussed in this thesis. In proton-proton interactions, Central Exclusive Production (CEP) is a process where the protons remain intact after the interaction, and an additional simple central system is produced. CEP processes are selected experimentally by requiring that there is no activity in the detector apart from the central system. The installation of additional detectors to increase the sensitivity at small angles from the beam axis is discussed. A geometrical description of the region of the LHC up to $100$~m on each side of the LHCb interaction point is developed. Simulated forward shower counters are added to the model, and the efficiencies of the detectors are measured. The main part of this thesis describes an analysis of CEP of $\chi_c$ mesons, reconstructed in the decay $\chi_c\to \gamma J/\psi$, $J/\psi\to \mu^+\mu^-$. The cross sections are measured using the dataset of $1\,\mathrm{fb^{-1}}$ collected by LHCb in 2011. The cross sections times branching ratios for $\chi_{c0}$, $\chi_{c1}$ and $\chi_{c2}$ are measured to be $2.2\pm 3.0\,\textrm{pb}$, $4.3\pm 7.6$~pb and $25.0\pm 9.2$~pb. This is consistent with theoretical predictions. A search for the CEP of $\chi_b$ mesons is also performed. A peak is observed in the mass spectrum, but it cannot be uniquely ascribed to $\chi_b$ CEP, because of background contributions which are not precisely determined. A limit is set on the sum of the $\chi_{b1}$ and $\chi_{b2}$ cross sections times branching ratios. Theoretical predictions for the cross section are at the level of $0.1$~fb, so no events are expected, and the data are consistent with this.