Studies of time-dependent $CP$ violation in charm decays of $B_s^0$ mesons

The thesis describes the world-first, time-dependent measurement of charge-parity ($CP$) violation in $B_s^0 \to D_s^\mp K^\pm$ decays. The study is performed at the LHCb experiment using data sample corresponding to an integrated luminosity of 1.0 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of $\sqrt{s} =7$ TeV, recorded in 2011. The $CP$ violating observables are found to be: $C = 0.52 \pm 0.25 \pm 0.04$, $D_{f} = 0.29 \pm 0.42 \pm 0.17$, $D_{\overline{f}} = 0.14 \pm 0.41 \pm 0.18$, $S_{f} = -0.90 \pm 0.31 \pm 0.06$, $S_{\overline{f}} = -0.36 \pm 0.34 \pm 0.06$, where the first (second) uncertainty is statistical (systematic). These observables are used to perform the first measurement of the Cabibbo-Kobayashi-Maskawa angle $\gamma$ in $B_s^0 \to D_s^\mp K^\pm$ decays, finding $\gamma = (113_{-44}^{+30})^\circ$~modulo $180^\circ$ at 68% CL, where the error contains both statistical and systematic uncertainties.