Measurement of $C\!P$ asymmetry in muon-tagged $D^0\rightarrow K^-K^+$ and $D^0\rightarrow \pi^-\pi^+$ decays at LHCb

This thesis presents the measurement of the time-integrated $C\!P$ asymmetries in $D^0\rightarrow K^-K^+$ and $D^0\rightarrow \pi^-\pi^+$ decays. The analysis uses data corresponding to an integrated luminosity of 3 $\mathrm{fb}^{-1}$ collected at the LHCb experiment in proton--proton collisions at centre-of-mass energies of 7 TeV and 8 TeV. The $D^0$ mesons are produced in semileptonic $b$-hadron decays, where the charge of the accompanying muon determines the initial flavour of the $D^0$ meson. By taking the difference of the observed asymmetries in the selected $D^0\rightarrow K^-K^+$ and $D^0\rightarrow \pi^-\pi^+$ samples, production and detection asymmetries cancel. The difference in $C\!P$ asymmetries between the two final states is measured to be \begin{equation} \Delta A_{C\!P} = A_{C\!P}(K^-K^+) - A_{C\!P}(\pi^-\pi^+) = (+0.14\pm 0.16(\text{stat}) \pm 0.08(\text{syst}))\,\%\;. \nonumber \end{equation} In order to obtain a measurement of $A_{C\!P}(K^-K^+)$ , large samples of Cabibbo-favoured $D$ meson decays are used to determine production and detection asymmetries to a high precision. The $C\!P$ asymmetry is found to be \begin{equation} A_{C\!P}(K^-K^+) = (-0.06\pm 0.15(\text{stat}) \pm 0.10(\text{syst}))\,\% \; ,\nonumber \end{equation} where the correlation coefficient between $\Delta A_{C\!P}$ and $A_{C\!P}(K^-K^+)$ is $\rho=0.28$. By combining these results, the $C\!P$ asymmetry in $D^0\rightarrow \pi^-\pi^+$ decays is derived to be $A_{C\!P}(\pi^-\pi^+) = (-0.20 \pm 0.19(\text{stat}) \pm 0.10(\text{syst}))\,\%$. The results of this thesis show that there is no significant $C\!P$ violation in $D^0\rightarrow K^-K^+$ and $D^0\rightarrow \pi^-\pi^+$ decays at the level of $10^{-3}$.