CP Violation and Lifetime Measurements of Two-body Charmless Decays of B Hadrons at LHCb

This thesis presents lifetime measurements of charmless two-body decays of b hadrons, specifically the decay modes known as $B\to h^+ h^{'-}$, where $B$ refers to meson or baryon containing a $b$ quark and $h^{(')}$ refers to a proton $p$, pion $\pi$ or kaon $K$. Using the large data samples collected by the LHCb detector, the $B\to h^+ h^{'-}$ channels with the largest branching fractions provide an opportunity to perform high-precision measurements of the properties of the decays. The leading-order processes in $B \rightarrow h^{+}h'^{-}$ decays are tree and penguin topologies, where the loop-dominated channels could be sensitive to non-standard model physics. The $B^0_S \to K^+ K^{-}$ mode is particularly interesting as it has a $CP$-even final state, as well as being dominated by penguin decay processes. The $B^0_S \to K^+ K^{-}$ effective lifetime can be used to calculate the $B_{s}^{0}$ decay-rate asymmetry $A_{\Delta \Gamma}$, which quantifies the amount of $CP$ violation in the decay. Using LHCb data with an integrated luminosity of 3 fb$^{-1}$ collected at centre of mass energies of 7 TeV and 8 TeV, the lifetimes of the decays $B^0_S \to K^+ K^{-}$, $B^0 \to K^+ \pi^{-}$, $B^0_S \to \pi^+ K^{-}$, $B^0 \to \pi^+ \pi^{-}$, $\Lambda^0_b \to p\pi^-$ and $\Lambda^0_b \to pK^-$ are measured to be \begin{alignat*}{6} \tau_{B^0_S \to K^+ K^{-}} = 1.410 \pm 0.009 \text{ ps (stat) } \pm 0.011 \text{ ps (syst)}, \\ \tau_{B^0 \to K^+ \pi^{-}} = 1.504 \pm 0.006 \text{ ps (stat) }\pm 0.023 \text{ ps (syst)}, \\ \tau_{B^0_S \to \pi^+ K^{-}} = 1.548 \pm 0.028 \text{ ps (stat) }\pm 0.023 \text{ ps (syst)}, \\ \tau_{B^0 \to \pi^+ \pi^{-}} = 1.495 \pm 0.012 \text{ ps (stat) }\pm 0.007 \text{ ps (syst)}, \\ \tau_{\Lambda^0_b \to p\pi^-} = 1.511 \pm 0.028 \text{ ps (stat) }\pm 0.012 \text{ ps (syst)}, \\ \tau_{\Lambda^0_b \to pK^-} = 1.477 \pm 0.022 \text{ ps (stat) }\pm 0.022 \text{ ps (syst)}. \end{alignat*} All these lifetime measurements are compatible with the current world averages. The decay-rate asymmetry is calculated to be \begin{equation*} A_{\Delta \Gamma}= -0.975 \pm 0.092{~(stat)} \pm 0.113{~(syst)} \pm 0.082{~(ext)}, \end{equation*} which agrees with the standard model prediction. A performance study measuring the photoelectron yield of the Ring Imaging Cherenkov (RICH) subdetector during 2012, 2015 and 2016 is also presented in this thesis. The RICH is used for particle identification and it distinguishes between pion, kaon and proton tracks. During the long shutdown between the 2012 and 2015 data taking periods, the aerogel in the RICH 1 detector was removed and the centre-of-mass energies of the proton-proton collisions increased from 7-8 TeV to 13 TeV. The photoelectron yield of RICH1 was found to increase by $\sim$ 3 photoelectrons in 2015 and 2016 and the photoelectron yield of RICH2 remained the same. This increase in RICH1 was expected due to the increased path length of the tracks through the Cherenkov medium once the aerogel was removed. Overall the contribution of photoelectron yield to the performance of the RICH remains acceptable for continued data taking.