Alignment of the LHCb Vertex Locator and Lifetime Measurements of Two-Body Hadronic Final States

Lifetime measurements offer excellent opportunities for precision tests of the Standard Model of Particle Physics as well as for discovery of effects involving particles beyond the Standard Model. This thesis presents a method for measurements of lifetimes and lifetime ratios and its application to two-body hadronic final states of heavy flavour decays at LHCb. The LHCb experiment is designed to measure heavy flavour particle decays produced in proton-proton collisions at the LHC. Key to high quality vertexing is the spatial alignment of the Vertex Locator. The algorithms designed for this task, including a novel approach for the relative sensor alignment, are discussed in detail. Their performance is presented using test beam data as well as data using the first beam induced tracks from LHC. The precision of these algorithms is found to be of the order of $1-2~ \mathrm{\mu{}m}$. A method for lifetime fitting using a Monte Carlo independent approach to determine a lifetime acceptance function on an event-by-event basis is presented. These acceptance functions are crucial to account for a bias caused by the trigger selection. The un-binned maximum likelihood fitter based on this method does not rely on a parametrised model for the lifetime distribution of combinatorial background. The fit of the lifetime measured in $B^0_s\to K^+K^-$ decays using a simulated data sample equivalent to an integrated luminosity of $0.1~ \mathrm{fb}^{-1}$ would yield $\tau(B^0_s\to K^+K^-) = (1.498\pm0.030_{stat.}\pm0.005_{syst.})~\mathrm{ps}$ with an average input lifetime of $1.500~\mathrm{ps}$. A competitive measurement of $\Delta\Gamma_s$ extracted from the $B^0_s \to K^+K^-$ lifetime measurement would require a data set equivalent to about $0.7\mathrm{fb}^{-1}$ of luminosity. With an integrated luminosity of only about $0.03\mathrm{fb}^{-1}$ it will be possible to make a competitive measurement of the $D$ mixing parameter $y_{\mathcal{CP}}$. This uses a lifetime ratio measurement with prompt $D^0\to h^+h'^-$ decays. A first event selection for prompt $D^0\to h^+h'^-$ decays is presented. The major hurdle for this measurement is the contribution from secondary $D$ decays. Possible solutions are discussed.