Performance of Hybrid Photon Detectors and Studies of Two-Body Hadronic B Decays at LHCb

The LHCb experiment at the CERN LHC accelerator will begin physics data taking in late 2009. LHCb aims to discover New Physics processes via precision measurements using heavy flavoured hadrons, such as $B$ and $D$ hadrons. This thesis describes studies relevant to measurements of $B$ decays to hadronic final states at LHCb. The Ring Imaging Cherenkov (RICH) counters of LHCb are crucial to the performance of such measurements. They use arrays of Hybrid Photon Detectors (HPDs) as their photodetection system. Detailed results are presented from the characterisation programme of the entire sample of 557 HPDs that were produced. Their overall performance is found to be outstanding, with only 2.2\% of HPDs judged to be unusable for the RICHes. The LHCb requirements and the contractual specifications are met and often exceeded in key areas. The measurement of the single photoelectron detection efficiency, $\eta$, of the HPD anode is described in detail. The efficiency was measured as $\eta=(87.9\pm 1.4)\%$. This value exceeds the LHCb-RICH requirement, and is in agreement with previous measurements. A method to measure the detector proper time resolution for two-body hadronic $B$ decays from data, making use of the per-event proper time error, is described. A proper time resolution model is proposed and is shown to accurately match the simulated resolution for these decays. The model parameters can be measured on data by fitting the flavour-tagged proper time distribution of the $B_s \rightarrow K^- \pi^+$ decay. Constraining the proper time resolution model via this method can potentially reduce systematic errors in time-dependent studies. A study is presented which examines the prospects of LHCb to discover new baryonic $B$ decay modes, with particular focus on the experimentally most promising mode, $B_d \rightarrow p \overline{p}$. It is found that a 5$\sigma$ discovery of $B_d \rightarrow p \overline{p}$ is possible with only 0.25 $\text{fb}^{-1}$ of nominal LHCb data, if its true branching fraction is close to the current experimental upper limit. Finally, the prospects of LHCb to measure the direct and mixing-induced $\mathcal{CP}$ asymmetries for the decay $B_d \rightarrow \pi^+ \pi^-$, via a time-dependent study, are assessed. A fit is made to the invariant mass and proper time distributions of simulated data. The total sensitivities with early data (0.3 $\text{fb}^{-1}$) are found to be 0.135(stat) + 0.012(syst) and 0.093(stat) + 0.018(syst) for the direct and mixing-induced asymmetries respectively. These sensitivities are competitive with current experimental measurements, and indicate that LHCb will come to dominate the world average values for these $\mathcal{CP}$ asymmetries as more data is collected.