Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>violation and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math>meson decay width difference with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mo mathvariant="bold">+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo mathvariant="bold">−</mml:mo></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mi>π</mml:mi><mml:mo mathvariant="bold">+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo mathvariant="bold">−</mml:mo></mml:msup></mml:math>decays (2013)

The time-dependent $CP$ asymmetry in ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ decays is measured using $pp$ collision data at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$, corresponding to an integrated luminosity of $1.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, collected with the LHCb detector. The decay-time distribution is characterized by the decay widths ${\ensuremath{\Gamma}}_{\mathrm{L}}$ and ${\ensuremath{\Gamma}}_{\mathrm{H}}$ of the light and heavy mass eigenstates of the ${B}_{s}^{0}\mathrm{\text{\ensuremath{-}}}{\overline{B}}_{s}^{0}$ system and by a $CP$-violating phase ${\ensuremath{\phi}}_{s}$. In a sample of 27 617 ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}{K}^{\ensuremath{-}}$ decays, where the dominant contribution comes from ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}$ decays, these parameters are measured to be ${\ensuremath{\phi}}_{s}=0.07\ifmmode\pm\else\textpm\fi{}0.09(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.01(\mathrm{syst})\text{ }\text{ }\mathrm{rad}$, ${\ensuremath{\Gamma}}_{s}\ensuremath{\equiv}({\ensuremath{\Gamma}}_{\mathrm{L}}+{\ensuremath{\Gamma}}_{\mathrm{H}})/2=0.663\ifmmode\pm\else\textpm\fi{}0.005(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.006(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$, and $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}\ensuremath{\equiv}{\ensuremath{\Gamma}}_{\mathrm{L}}\ensuremath{-}{\ensuremath{\Gamma}}_{\mathrm{H}}=0.100\ifmmode\pm\else\textpm\fi{}0.016(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.003(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$, corresponding to the single most precise determination of ${\ensuremath{\phi}}_{s}$, $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}$, and ${\ensuremath{\Gamma}}_{s}$. The result of performing a combined analysis with ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays gives ${\ensuremath{\phi}}_{s}=0.01\ifmmode\pm\else\textpm\fi{}0.07(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.01(\mathrm{syst})\text{ }\text{ }\mathrm{rad}$, ${\ensuremath{\Gamma}}_{s}=0.661\ifmmode\pm\else\textpm\fi{}0.004(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.006(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$, and $\ensuremath{\Delta}{\ensuremath{\Gamma}}_{s}=0.106\ifmmode\pm\else\textpm\fi{}0.011(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.007(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$. All measurements are in agreement with the Standard Model predictions.