Measurement of Indirect CP Violation in Charm at LHCb

This thesis describes two pieces of work. The first is a study of the resolution of the LHCb vertex locator throughout Run 1. The second comprises analyses to measure the charm mixing and $CP$ violation observables $A_{\Gamma}$ and $y_{CP}$. An estimate of the resolution of the LHCb vertex locator is required for use in the track fits. A method to measure the resolution with collision data has been developed and tested. The performance of the sub-detector throughout Run 1 of the LHC has been assessed. A significant degrading of the resolution has been seen. The effects of this on the track reconstruction has been examined with little change in the measured quantities being observed. The measurement of indirect $CP$ violation in neutral $D$ meson transitions has been measured through the observables $A_{\Gamma}$ and $y_{CP}$, using $fb^{-1}$ of $pp$ collisions with a centre of mass energy $7 TeV$, collected by the LHCb detector in 2011. $A_{\Gamma}$ describes the $CP$ asymmetry of the lifetime of the $D^0$ decaying to a $CP$ eigenstate $(K^+K^-$ or $\pi^+ \pi^-)$. The analysis documented here yields $A_{\Gamma} = (-0.17\pm0.54)\times 10^{-3}$ when the measurements are combined. This is the world's best result and represented a factor of four improvement over the previous best measurement. The observable $y_{CP}$ compares the effective lifetimes of the Cabibbo favoured decay $D^0 \to K^- \pi^+$ and the transition to a $CP$ eigenstate $(K^+K^-$ or $\pi^+ \pi^-)$. The unblinded result obtained in this document, averaged over both final states is $y_{CP} = (5.61\pm1.56)\times 10^{-3}$. This result is commensurate with the world average central value within 1.25 standard deviations and has significance of $3.6\,\sigma$ relative to zero.