Measurement of time-dependent $CP$ violation in charmless two-body $B$ decays

Using an integrated luminosity of 0.69~fb$^{-1}$ collected by LHCb in 2011, we report measurements of direct and mixing-induced $C\!P$ violation in $B^0\to\pi^+\pi^-$ and $B^0_s\to K^+K^-$ decays. We obtain \begin{equation*} \begin{split} A^{\rm dir}_{\pi\pi} = 0.11 \pm 0.21 \pm 0.03,\\ A^{\rm mix}_{\pi\pi} = -0.56 \pm 0.17 \pm 0.03,\\ A^{\rm dir}_{KK} = 0.02 \pm 0.18 \pm 0.04,\\ A^{\rm mix}_{KK} = 0.17 \pm 0.18 \pm 0.05, \end{split} \end{equation*} where the first uncertainties are statistical and the second systematic. The correlations are found to be $\rho (A^{\rm dir}_{\pi\pi},\,A^{\rm mix}_{\pi\pi})=-0.34$ and $\rho(A^{\rm dir}_{KK},\,A^{\rm mix}_{KK})=-0.10$. The measurements of $A^{\rm dir}_{\pi\pi}$ and $A^{\rm mix}_{\pi\pi}$ are compatible with those from the $B$ factories and yield 3.2$\sigma$ evidence of mixing-induced $C\!P$ violation, whereas $A^{\rm dir}_{KK}$ and $A^{\rm mix}_{KK}$ are measured for the first time ever.