The time-dependent $CP$ asymmetry in $B_s^0\to J/\psi K^{+}{K}^{-}$ decays is measured using $pp$ collision data, corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96 000 $B_s^0\to J/\psi K^{+}{K}^{-}$ decays, the $CP$-violating phase ${\varphi }_s$ is measured, as well as the decay widths ${\mathrm{\Gamma }}_{\mathrm{L}}$ and ${\mathrm{\Gamma }}_{\mathrm{H}}$ of the light and heavy mass eigenstates of the $B_s^0–{\overline{B}}_s^0$ system. The values obtained are ${\varphi }_s=-0.058\pm 0.049\pm 0.006\mathrm{rad}$, ${\mathrm{\Gamma }}_s\equiv ({\mathrm{\Gamma }}_{\mathrm{L}}+{\mathrm{\Gamma }}_{\mathrm{H}})/2=0.6603\pm 0.0027\pm 0.0015{\mathrm{ps}}^{-1}$, and $\mathrm{\Delta }{\mathrm{\Gamma }}_s\equiv {\mathrm{\Gamma }}_{\mathrm{L}}-{\mathrm{\Gamma }}_{\mathrm{H}}=0.0805\pm 0.0091\pm 0.0032{\mathrm{ps}}^{-1}$, where the first uncertainty is statistical and the second, systematic. These are the most precise single measurements of those quantities to date. A combined analysis with $B_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays gives ${\varphi }_s=-0.010\pm 0.039\mathrm{rad}$. All measurements are in agreement with the standard model predictions. For the first time, the phase ${\varphi }_s$ is measured independently for each polarization state of the $K^{+}{K}^{-}$ system and shows no evidence for polarization dependence.

• Received 12 November 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.041801

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© 2015 CERN, for the LHCb Collaboration