Introduction

Abstract

An accurate determination of the angle $\gamma$ of the Unitary Triangle is one of the most important goals of the LHCb experiment. The LHCb detector is a single-arm spectrometer at the LHC, optimised for beauty and charm flavour physics. As the angle $\gamma$ is the least experimentally constrained parameter of the Unitary Triangle, its precise experimental determination can be used to test the validity of the Standard Model. The Unitary Triangle phase $\gamma$ can be extracted in $B \rightarrow DK$ decays at tree-level, exploiting the interference between $b \rightarrow c(\bar{u}s)$ and $b \rightarrow u(\bar{c}s)$ transitions. This interference is sensitive to $\gamma$ and can give measurable charge asymmetries. In particular, $\gamma \ne 0$ is required to produce direct $C \! P$ violation in $B$ decays and this is the only $C \! P$-violating mechanism for the decay of charged $B^\pm$ mesons. In this thesis, an analysis of $C \! P$ violation in $B^{\pm } \rightarrow DK^{\pm }$ and $B^{\pm } \rightarrow D\pi ^{\pm }$ decays is presented, where the $D$ meson is reconstructed in the two-body final states: $K^{\pm }\pi ^{\mp }$, $K^+K^-$, $\pi ^+\pi ^-$ and $\pi ^{\pm }K^{\mp }$. The analysis uses the full 2011 LHCb dataset of 1.0${\text {fb}}^{-1}$, collected from $pp$ collisions at $\sqrt{s}$ = 7$\mathrm \,TeV$. Several $C \! P$-related quantities, e.g. the ratio of $B \rightarrow DK$ and $B \rightarrow D\pi$ branching fractions and their charge asymmetries, are measured via a simultaneous fit to the invariant mass distributions of the modes considered. The suppressed $B^{\pm }\rightarrow DK^{\pm }$ mode is observed for the first time with $\approx 10\sigma$ significance. Once all measurements are combined, direct $C \! P$ violation is established in $B^{\pm }$ decays with a total significance of $5.8\sigma$. The measured $C \! P$ observables are summarised here with their statistical uncertainties and assigned systematic uncertainties:

$$\begin{aligned} R_{C \! P +}&= 1.007 \pm 0.038 \pm 0.012 \\ A_{C \! P +}&= 0.145 \pm 0.032 \pm 0.010 \\ R_{\mathrm{ADS}(K)}&= 0.0152 \pm 0.0020 \pm 0.0004 \\ A_{\mathrm{ADS}(K)}&= -0.52 \pm 0.15 \pm 0.02 \\ R_{\mathrm{ADS}(\pi )}&= 0.00410 \pm 0.00025 \pm 0.00005 \\ A_{\mathrm{ADS}(\pi )}&= 0.143 \pm 0.062 \pm 0.011 \end{aligned}$$