Measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> asymmetries in two-body <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>-meson decays to charged pions and kaons

The time-dependent $CP$ asymmetries in ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ decays are measured using a data sample of $p$ $p$ collisions corresponding to an integrated luminosity of $3.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The same data sample is used to measure the time-integrated $CP$ asymmetries in ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{\ensuremath{-}}$ decays. The results are ${C}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}}=\ensuremath{-}0.34\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.01$, ${S}_{{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}}=\ensuremath{-}0.63\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\pm\else\textpm\fi{}0.01$, ${C}_{{K}^{+}{K}^{\ensuremath{-}}}=0.20\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.02$, ${S}_{{K}^{+}{K}^{\ensuremath{-}}}=0.18\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.02$, ${A}_{{K}^{+}{K}^{\ensuremath{-}}}^{\mathrm{\ensuremath{\Delta}}\mathrm{\ensuremath{\Gamma}}}=\ensuremath{-}0.79\ifmmode\pm\else\textpm\fi{}0.07\ifmmode\pm\else\textpm\fi{}0.10$, ${A}_{CP}^{{B}^{0}}=\ensuremath{-}0.084\ifmmode\pm\else\textpm\fi{}0.004\ifmmode\pm\else\textpm\fi{}0.003$, and ${A}_{CP}^{{B}_{s}^{0}}=0.213\ifmmode\pm\else\textpm\fi{}0.015\ifmmode\pm\else\textpm\fi{}0.007$, where the first uncertainties are statistical and the second systematic. Evidence for $CP$ violation is found in the ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ decay for the first time.