Measurement of $CP$ violation and the $B_s^0$ meson decay width difference with $B_s^0 \to J/\psi K^+K^-$ and $B_s^0\to J/\psi\pi^+\pi^-$ decays

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