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The decay-time-dependent $CP$ asymmetry in $B^0_s\to J/\psi(\to\mu^{+}\mu^{-}) K^{+}K^{-}$ decays is measured using proton-proton collisiondata, corresponding to an integrated luminosity of 6 $fb^{-1}$, collected withthe LHCb detector at a center-of-mass energy of 13 TeV. Using a sample ofapproximately 349 000 $B^{0}_{s}$ signal decays with an invariant $K^{+}K^{-}$mass in the vicinity of the $\phi(1020)$ resonance, the $CP$-violating phase$\phi_s$ is measured, along with the difference in decay widths of the lightand heavy mass eigenstates of the $B^0_s$-$\bar{B}^0_s$ system,$\Delta\Gamma_s$, and the difference of the average $B^0_s$ and $B^0$ mesondecay widths, $\Gamma_s-\Gamma_d$. The values obtained are $\phi_s = \ -0.039\pm 0.022 \pm 0.006$ rad, $\Delta\Gamma_s = 0.0845 \pm 0.0044 \pm 0.0024 $ps$^{-1}$ and $\Gamma_s-\Gamma_d = -0.0056 ^{+ 0.0013}_{-0.0015} \pm 0.0014$ps$^{-1}$, where the first uncertainty is statistical and the secondsystematic. These are the most precise single measurements to date and areconsistent with expectations based on the Standard Model and with the previousLHCb analyses of this decay. These results are combined with previousindependent LHCb measurements. The phase $\phi_s$ is also measuredindependently for each polarization state of the $K^{+}K^{-}$ system and showsno evidence for polarization dependence.

Improved measurement of $CP$ violation parameters in $B^0_s\to J/\psi K^{+}K^{-}$ decays in the vicinity of the $\phi(1020)$ resonance