Measurement of $CP$ observables in $B^0\to D K^{*0}$ with $D\to K^+K^-$

The decay $B^0 \to D K^{*0}$ and the charge conjugate mode are studied using 1.0${\mathrm fb}^-1$ of $pp$ collision data collected by the LHCb experiment at $\sqrt{s} = 7TeV$ in 2011. The CP asymmetry between the $B^0 \to D K^{*0}$ and the $\bar{B}^0 \to D \bar{K }^{*0}$ decay rates, with the neutral D meson in the CP-even final state $K^+K^-$, is found to be \begin{equation*} {\cal A}_d^{KK} = -0.45 \pm 0.23 \pm 0.02, \end{equation*} where the first uncertainty is statistical and the second is systematic. In addition, favoured $B^0 \to D K^{*0}$ decays are reconstructed with the $D$ meson in the non-$CP$ eigenstate $K^+ \pi^-$. The ratio of the $B$-flavour averaged decay rates in $D$ decays to $CP$ and non-$CP$ eigenstates is measured to be \begin{equation*} {\cal R}_d^{KK} = 1.36\,^{+0.37}_{ -0.32} \pm 0.07, \end{equation*} where the ratio of the branching fractions of $D^0 \to K^- \pi^+$ to $D^0 \to K^+ K^-$ decays is included as multiplicative factor. The CP asymmetries measured with two control channels, the favoured $B^0 \to DK^{*0}$ decay with $D \to K^+ \pi^-$ and the $\bar{B}_s^0 \to D K^{*0}$ decay with $ D \to K^+ K^-$, are also reported.