Measurement of CP asymmetries in ${\bar{B}}^0\to D_s^{-}{D}^{+}$ and ${\bar{B}}_s^0\to D_s^{+}{D}^{-}$ decays

Measurements of the combined CP asymmetries in ${\bar{B}}^0\to D_s^{-}{D}^{+}$ and ${\bar{B}}_s^0\to D_s^{+}{D}^{-}$ decays are made using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9fb${}^{-1}$. The measurements are found to be \begin{aligned} A_{CP}(\kern 0.18em\overline{\kern -0.18em B}^0 \to D_s^- D^+) &= 0.0009 \pm 0.0053 \pm 0.0040, \ A_{CP}(\kern 0.18em\overline{\kern -0.18em B}_s^0 \to D_s^+ D^-) &= 0.103\phantom{0} \pm 0.053\phantom{0} \pm 0.010, \end{aligned} where the first and second uncertainties are statistical and systematic, respectively. This is the first measurement of this asymmetry in ${\bar{B}}_s^0$ decays, and the most precise measurement to date for ${\bar{B}}^0$ decays. Both measurements are found to be consistent with CP symmetry.