Precision measurement of $CP$ violation in $B_s^0\to J\mathrm{/}\psi K^{+}{K}^{-}$ decays

The time-dependent $CP$ asymmetry in $B_s^0\to J\mathrm{/}\psi K^{+}{K}^{-}$ decays is measured using $pp$ collision data, corresponding to an integrated luminosity of $3.0$fb${}^{-1}$, collected with the LHCb detector at centre-of-mass energies of $7$ and $8$TeV. In a sample of 96 000 $B_s^0\to J\mathrm{/}\psi K^{+}{K}^{-}$ decays, the $CP$-violating phase ${\varphi }_s$ is measured, as well as the decay widths ${\mathrm{\Gamma }}_L$ and ${\mathrm{\Gamma }}_H$ of the light and heavy mass eigenstates of the $B_s^0-{\bar{B}}_s^0$ system. The values obtained are $\phi_s = -0.058 \pm 0.049 \pm 0.006$rad,$\Gamma_s \equiv (\Gamma_{L}+\Gamma_{H})/2 = 0.6603 \pm 0.0027 \pm 0.0015$ps$^{-1}$,and$\Delta\Gamma_s \equiv \Gamma_{L} - \Gamma_{H} = 0.0805 \pm 0.0091 \pm 0.0032$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 $B_s^{0} \to J/\psi \pi^+\pi^-$decaysgives$\phi_s = -0.010 \pm 0.039 $rad. All measurements are in agreement with the Standard Model predictions. For the first time the phase ${\varphi }_s$ is measured independently for each polarisation state of the $K^{+}{K}^{-}$ system and shows no evidence for polarisation dependence.