Precision measurement of the CKM parameter sin (𝟮𝝱) with the LHCb experiment

This thesis presents a decay-time dependent measurement of CP violation in the decay of $B^0$ and $\bar{B}^0$ mesons into their common $J\!/\!\psi K_\text{S}^0$ final state. The CP observables $S_{J\!/\!\psi K_\text{S}^0}$ and $C_{J\!/\!\psi K_\text{S}^0}$ allow access to the magnitude of the symmetry violation in the interference between the $B$ meson decay and mixing amplitudes and can directly be related to the CKM angle $\beta$. Using a dataset of selected signal $B^0\rightarrow J\!/\!\psi K_\text{S}^0$ candidates corresponding to an integrated luminosity of $3.0\,\text{fb}^{-1}$ collected at centre-of-mass energies of $7$ and $8\,\text{TeV}$ by the LHCb experiment, the CP observables are measured to be % \begin{equation*} \begin{split} S_{J\!/\!\psi K_S} &= \phantom{-}0.731 \pm 0.035\,(\text{stat.}) \pm 0.020\,(\text{syst.}),\ \text{and} \\ C_{J\!/\!\psi K_S} &= -0.038 \pm 0.032\,(\text{stat.}) \pm 0.005\,(\text{syst.}), \end{split} \end{equation*} % resulting in the worlds most precise measurement of these quantities at a hadron collider. With the parameter $C_{J\!/\!\psi K_\text{S}^0}$ fixed to zero, $S_{J\!/\!\psi K_\text{S}^0}$ equals $\sin(2\beta) = 0.746 \pm 0.030\,(\text{stat.})$. The results have a similar precision as previous measurements at the $B$ factories Babar and Belle and are consistent with these and with expectations from measurements of other CKM matrix parameters.