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The time-dependent $CP$ asymmetries of $B^0\to \pi^+\pi^-$ and$B^0_\mathrm{s}\!\to K^+K^-$ decays are measured using a data sample of $pp$collisions corresponding to an integrated luminosity of 1.9 fb$^{-1}$,collected with the LHCb detector at a centre-of-mass energy of 13 TeV. Theresults are \begin{eqnarray*} C_{\pi\pi} & = & -0.311 \pm 0.045 \pm 0.015, \\S_{\pi\pi} & = & -0.706 \pm 0.042 \pm 0.013, \\ C_{KK} & = & \phantom{-}0.164\pm 0.034 \pm 0.014, \\ S_{KK} & = & \phantom{-}0.123 \pm 0.034 \pm 0.015, \\\cal {A}^{\mathrm{\Delta\Gamma}}_{\mathit{KK}} & = & -0.83\phantom{0} \pm0.05\phantom{0} \pm 0.09, \end{eqnarray*} where the first uncertainties arestatistical and the second systematic. The same data sample is used to measurethe time-integrated $CP$ asymmetries of $B^0\to K^+\pi^-$ and$B^0_\mathrm{s}\to K^-\pi^+$ decays and the results are \begin{eqnarray*}A_{CP}^{B^0} & = & -0.0824 \pm 0.0033 \pm 0.0033, \\ A_{CP}^{B^0_\mathrm{s}} &= & \phantom{-}0.236\phantom{0} \pm 0.013\phantom{0} \pm 0.011. \end{eqnarray*}All results are consistent with earlier measurements. A combination of LHCbmeasurements provides the first observation of time-dependent $CP$ violation in$B^0_\mathrm{s}$ decays.

Observation of $CP$ violation in two-body $B_{(\mathrm{s})}^{\,0}$-meson decays to charged pions and kaons