CP Violation studies of $B\to DD$ channels using the LHCb detector

LHCb is one of five experiments which will start data-taking at the Large Hadron Collider (LHC) in 2007. LHCb is a B-physics and rare decay experiment, with the aim to throughly test the internal consistency of the Standard Model, and in particular, to over-constrain the parameters of the CKM matrix and the unitarity triangle. This thesis outlines the main goals of the LHCb experiment, followed by a review of the theoretical background upon which physics at the LHCb experiment is based. The detector design of the LHCb experiment is also described, with emphasis placed upon the Ring-Imaging Cherenkov (RICH) detectors. The photon detector choice for the RICH is the pixel Hybrid Photon Detector (HPD). Studies of the performance of a 10 MHz full-scale prototype pixel HPD are presented and despite significant bump-bond degradation during manufacture, its behaviour is shown to be consistent with that of previous prototypes. A method for determining the pixel HPD detection efficiency to single photoelectrons is outlined. The prototype was determined to have an efficiency of 0.827 +- 0.001 (stat) +- 0.037 (syst). This figure is compared to the minimum requirement of ~85 % criteria set by LHCb for the choice of the RICH photodetector technology. Analysis software for B -> DD channels; B->D+D-, Bs->Ds+Ds- and Bc+ -> Ds+D~0 have been implemented and simulation studies carried out. Studies of these channels were motivated by two proposed theoretical methods to determine the sensitivity to the CKM angle $\gamma$. One proposed method is that $\gamma$ can be extracted from a measurement of the time dependent B->D+D- rate provided that the overall normalisation is fixed using the CP-averaged Bs->Ds+Ds- rate and assuming that the CKM angle beta is known. It has also been proposed that $\gamma$ can also be extracted from amplitude relations in the measurement of Bc+ -> Ds+D~0 decays. For each of these channels the optimised cuts and the resulting annual event yields are presented. The trigger and flavour tagging performance have also been investigated. It is shown that the $\Bddecay$ and $\Bsdecay$ channels can be detected, reconstructed, selected and triggered with efficiencies of 0.107 +- 0.09 % and 0.091 +- 0.08 % respectively. This results in annual triggered event yields of 2.6 +- 0.2 k/year and 2.8 +- 0.3 k/year. Assuming that inclusive bb~ events are the dominant source of combinatorial background then an upper limit to the background-to-signal ratio (B/S) of Ds+D~0 channel show that it is unlikely that this channel could be used to study gamma and the Bc mass and lifetime at LHCb. Some of the work presented here has previously been published elsewhere