A study of $B \to K\pi$ decays with the LHCb experiment

LHCb is a b-physics detector experiment which will take data at the 14 TeV LHC accelerator at CERN from 2007 onward. In this thesis I present two main areas of work relating to LHCb; firstly an investigation of a novel pattern recognition method in the LHCb RICH detectors and secondly a study of LHCb's potential to reconstruct and identify B -> K pi decays. The pattern recognition studies presented here make use of a Markov Chain sampler to identify Cerenkov rings on a detector pixel array. The method presented does not use the tracking information required by the standard LHCb particle identification system. Studies have been performed to characterise the performance of the trackless ring-finder in the RICH2 detector and to investigate the sources of untracked rings. The ring-finder performance is seen to seriously degrade in high-occupancy regions, indicating that tracking information is required for realistic particle ID in LHCb. The sampler has also been integrated into the RICH2 background-estimation system, which permits robustness studies of the RICH particle ID system. Finally, I show that particle identification performance can be improved by use of the ring sampler for background estimation. The study of B -> K pi decays also makes use of a multi-variable sampler, used to optimise the signal significance of signal-selection cuts. Using several types of cut definition, cut sets have been determined which show that LHCb expects to reconstruct (90.0 ± 6.2)k B0d -> K+ pi- decays and (6.9 ± 0.6)k B+ -> K0S (pi+ pi-) pi+ decays in a year of operation with optimal signal significance. Robustness tests of the selection variables show the cuts to be largely resilient to systematic shifts of ±20% around the optimised values, although the data set is statistically limiting. It is anticipated that, in its first year of operation, LHCb will improve the statistical precision on the CP observables for B -> K pi decays by an order of magnitude over that currently offered by the b-factories. The branching ratios of the considered B -> K pi processes can be used, in principle, to both bound and to constrain the CKM weak phase gamma. The predicted experimental uncertainties after one year of LHCb data-taking will tightly restrict the CKM gamma constraint, offering statistical errors of Delta{gamma} \in [0.3, 2.9] deg. However, the value of gamma depends strongly on theoretical predictions of penguin-to-tree process amplitude ratios and the theoretical uncertainty on this renders the method unhelpful at present, placing an additional variation on gamma of ~50 deg. Hence, these decays are identified for now as more useful in enabling LHCb to constrain the effects of new physics in electroweak penguin loops than as a direct method to measure gamma.