Measurement of the CP Violating Phase $\phi_s$ and the Decay Width Difference $\Delta\Gamma_s$ in the Decay $B^0_s \rightarrow J/\psi\phi$ with the ATLAS Experiment

A feature of the neutral $B^0_s$ meson is that it can oscillate into its antiparticle before it decays, which can give rise to CP violation due to interference of the two processes mixing and decay. The time-dependent $B^0_s \rightarrow J/\psi\phi$ decay is characterized by the decay width $\Gamma_s$ and the decay width difference $\Delta\Gamma_s$. The $B^0_s - \bar{B}^0_s$ oscillation is governed by the mass difference $\Delta m_s$, and the CP violation is described by the relative phase $\phi_s$ between the mixing and the decay. The analysis of the decay channel provides the possibility to test the predictions of the Standard Model of particle physics for those parameters. In particular the measurement of the CP violating phase $\phi_s$ has the capability to unveil enhancement of the small Standard Model value by New Physics. In this thesis the measurement of $\phi_s$, $\Gamma_s$ and $\Delta\Gamma_s$ in the decay $B^0_s \rightarrow J/\psi\phi$ is presented. The analysis makes use of an integrated luminosity of $4.9 \ fb^{-1}$ that was collected with the ATLAS detector in $p-p$ collision produced by the LHC at a center-of-mass energy of $\sqrt{s} = 7\ TeV$. After the reconstruction and selection of the decay channel, a time-dependent angular analysis of the $B^0_s \rightarrow J/\psi\phi$ decay is performed. An untagged as well as a tagged analysis, using opposite side flavor tagging to determine the production flavor of the $B^0_s$ mesons, are presented. The parameters of interest are extracted through the application of an unbinned maximum likelihood fit method, which takes detector efficiency and resolution effects into account. A possible contribution from S-wave decays to the data sample as well as the contamination due to reflections from $B^0_d$ decays are incorporated in the fit. The result of the measurement is found to be consistent with the Standard Model prediction and is presented as $68 \ \% $, $90 \ \% $ and $95 \ \% $ confidence regions in the $\phi_s - \Delta\Gamma_s$ plane.