| Summary: | The <em>CP</em> violating phase <em>β<sup>J/ψφ</sup><sub style="position: relative; left: -2.0em;">s</sub></em> is measured in decays of <em>B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub> &rightarrow; <em>J/ψφ</em>. This measurement uses 5.2 fb<sup>-1</sup> of data collected in √<sup><sup>—</sup></sup><sub style="position:relative;left: -.5em;"><em>s</em></sub> = 1.96 TeV <em>p̅p</em> collisions at the Fermilab Tevatron with the CDF Run-II detector. <em>CP</em> violation in the <em>B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub>-<em>̅B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub>bar system is predicted to be very small in the Standard Model. However, several theories beyond the Standard Model allow enhancements to this quantity by heavier, New Physics particles entering second order weak mixing box diagrams. Previous measurements have hinted at a deviation from the Standard Model expectation value for <em>β<sup>J/ψφ</sup><sub style="position: relative; left: -2.0em;">s</sub></em> with a significance of approximately 2σ. The measurement described in this thesis uses the highest statistics sample available to date in the <em>B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub> rightarrow; <em>J/ψφ</em> decay channel, where <em>J/ψ &rightarrow; μ<sup>&plus;</sup> μ<sup>−</sup></em> and <em>φ</em> &rightarrow; <em>K<sup>&plus;</sup>K<sup>−</sup></em>. Furthermore, it contains several improvements over previous analyses, such as enhanced signal selection, fully calibrated particle ID and flavour tagging, and the inclusion of an additional decay component in the likelihood function. The added decay component considers <em>S</em>-wave states of <em>KK</em> pairs in the <em>B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub> &rightarrow; <em>J/ψK<sup>&plus;</sup>K<sup>−</sup></em> channel. The results are presented as 2-dimensional frequentist confidence regions for <em>β<sup>J/ψφ</sup><sub style="position: relative; left: -2.0em;">s</sub></em> and ΔΓ (the width difference between the <em>B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub> mass eigenstates), and as a confidence interval for <em>β<sup>J/ψφ</sup><sub style="position: relative; left: -2.0em;">s</sub></em> of [0.02,0.52] Ｕ [1.08, 1.55] at the 68 % confidence level. The measurement of the <em>CP</em> violating phase obtained in this thesis is complemented by the world's most precise measurement of the lifetime <em>τ<sub>s</sub></em> = 1.53 &pm; 0.025 (stat.) &pm; 0.012 (syst.) ps and decay width difference ΔΓ = 0.075 &pm; 0 .035 (stat.) &pm; 0.01 (syst.) ps<sup>−1</sup> of the <em>B</em><sup>0</sup><sub style="position: relative; left: -0.5em;">s</sub> meson, with the assumption of no <em>CP</em> violation.
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