Measurement of $CP$ Violation in $B^0 \to J/\psi K_{S}^0$ Decays with the LHCb Experiment

This thesis presents the LHCb measurement of $CP$ violation in decays of neutral $B^0$ mesons and their anti-particles into the $J/\psi K_{S}^{0}$ final state. The interference of the $B^{0}$--$\overline{B}^{0}$ mixing with the decay into the common final state leads to a decay time dependent decay rate asymmetry between $B^{0}$ and $\overline{B}^{0}$ mesons. The $CP$ observables, $S_{J/\psi K_{S}^{0}}$ and $C_{J/\psi K_{S}^{0}}$, allow for a determination of the CKM angle $\beta$, which is one of the most precisely measured $CP$ parameters of the Standard Model. Thus, $B^{0}\to J/\psi K_{S}^{0}$ represents an excellent reference channel for decay time dependent $CP$ measurements at LHCb. The analysis is performed with a dataset that corresponds to $1\text{ fb}^{-1}$ of $pp$ collisions collected at a centre-of-mass energy of $7\text{ TeV}$ by the LHCb experiment at CERN. Using an unbinned maximum likelihood fit, the $CP$ observables are measured as \begin{equation*} \begin{aligned} S_{J/\psi K_{S}^{0}} &= 0.73 \pm 0.07 \,\text{(stat.)} \pm 0.04 \,\text{(syst.)} \quad \text{and} \\ C_{J/\psi K_{S}^{0}} &= 0.03 \pm 0.09 \,\text{(stat.)} \pm 0.01 \,\text{(syst.)} \ , \end{aligned} \end{equation*} leading to the world's best measurement of these observables at a hadron collider. Furhermore, these results are consistent with the averages of previous measurements and within expectations from the Standard Model.