Measurement of CP violation in two-body b-hadron decays with the LHCb experiment

The LHCb experiment has been designed to perform flavour-physics measurements at the Large Hadron Collider. Measurements of $C\!P$-violation are of great importance to shed light on some theoretical open issues and to find evidence for physics beyond the Standard Model of particle physics. Using a data sample corresponding to an integrated luminosity of about 3.0 fb$^{-1}$ collected by the LHCb experiment during the LHC Run-1, various $C\!P$-violation measurements with two-body $b$-hadron decays are performed, along with some subsidiary measurements. The $b$-hadron production asymmetries in the LHCb acceptance are measured to be \begin{eqnarray} A_\mathrm{P}(B^+)_{\sqrt{s} = 7\ \mathrm{TeV}}&=&-0.002 \pm 0.002 \pm 0.004 \nonumber ,\\ A_\mathrm{P}(B^+)_{\sqrt{s} = 8\ \mathrm{TeV}}&=&-0.007 \pm 0.002 \pm 0.003 \nonumber ,\\ A_\mathrm{P}(B^0)_{\sqrt{s} = 7\ \mathrm{TeV}}&=& \phantom{-}0.004 \pm 0.009 \pm 0.001 , \nonumber \\ A_\mathrm{P}(B^0)_{\sqrt{s} = 8\ \mathrm{TeV}}&=&-0.014 \pm 0.006 \pm 0.001 \nonumber ,\\ A_\mathrm{P}(B^0_s)_{\sqrt{s} = 7\ \mathrm{TeV}}&=&-0.007 \pm 0.029 \pm 0.006 \nonumber ,\\ A_\mathrm{P}(B^0_s)_{\sqrt{s} = 8\ \mathrm{TeV}}&=&\phantom{-}0.020 \pm 0.019 \pm 0.006 ,\nonumber \\ A_\mathrm{P}(\Lambda^0_b)_{\sqrt{s} = 7\ \mathrm{TeV}}&=&-0.001 \pm 0.025 \pm 0.011 \nonumber ,\\ A_\mathrm{P}(\Lambda^0_b)_{\sqrt{s} = 8\ \mathrm{TeV}}&=&\phantom{-}0.034 \pm 0.016 \pm 0.008 , \nonumber \end{eqnarray} where the first uncertainties are statistical and the second systematic. In particular, the measurement of the $\Lambda^0_b$ production asymmetry provides a necessary ingredient for the determination of the physical $C\!P$ asymmetries in $\Lambda^0_b \to p K^-$ and $\Lambda^0_b \to p \pi^-$ decays. These quantities are found to be \begin{eqnarray} A_\mathrm{CP}(\Lambda^0_b \to p K^-) &=& -0.019 \pm 0.013 \pm 0.017 , \nonumber \\ A_\mathrm{CP}(\Lambda^0_b \to p \pi^-) &=& -0.035 \pm 0.017 \pm 0.018 , \nonumber \end{eqnarray} where the first uncertainties are statistical and the second systematic. Finally, the direct and mixing-induced $C\!P$-violating asymmetries in $B^0 \to \pi^+ \pi^-$ and $B^0_s \to K^+ K^-$ decays are measured, together with the direct $C\!P$ asymmetries in $B^0 \to K^+ \pi^-$ and $B^0_s \to \pi^+ K^-$ decays. The results are \begin{eqnarray} C_{\pi\pi} & = & -0.34 \pm 0.06 \pm 0.01,\nonumber\\ S_{\pi\pi} & = & -0.63 \pm 0.05 \pm 0.01,\nonumber\\ C_{KK} & = & \phantom{-}0.20 \pm 0.06 \pm 0.02,\nonumber\\ S_{KK} & = & \phantom{-}0.18 \pm 0.06 \pm 0.02,\nonumber\\ A^{\Delta\Gamma}_{KK} & = & -0.79 \pm 0.07 \pm 0.10, \nonumber\\ A_\mathrm{CP}(B^0 \to K^+ \pi^-) & = & -0.084 \pm 0.004 \pm 0.003, \nonumber\\ A_\mathrm{CP}(B^0_s \to \pi^+ K^-) & = & \phantom{-}0.213 \pm 0.015 \pm 0.007,\nonumber \end{eqnarray} where the first uncertainties are statistical and the second systematic. All these $C\!P$-violation measurements are compatible with the world averages and improve on previous determinations.