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

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. The results are \begin{eqnarray*} C_{\pi\pi} & = & -0.311 \pm 0.045 \pm 0.015, \newline S_{\pi\pi} & = & -0.706 \pm 0.042 \pm 0.013, \newline C_{KK} & = & \phantom{-}0.164 \pm 0.034 \pm 0.014, \newline S_{KK} & = & \phantom{-}0.123 \pm 0.034 \pm 0.015, \newline \cal {A}^{\Delta\Gamma}_{KK} & = & -0.83\phantom{0} \pm 0.05\phantom{0} \pm 0.09, \end{eqnarray*} where the first uncertainties are statistical and the second systematic. The same data sample is used to measure the 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, \newline 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 LHCb measurements provides the first observation of time-dependent $CP$ violation in $B^0_\mathrm{s}$ decays.