A study of CP violation and measurement of the CKM angle γ in B0→ DK∗0 decays

Two measurements of CP observables in $B^0 \to DK^{∗0}$ decays are presented, where $D$ represents a superposition of $D^0$ and $\overline{D}^0$ states. The measurements use samples of proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV. The first measurement uses 5 fb$^{−1}$ of data with the D meson reconstructed in the two-body final states $K^+\pi^-$, $\pi^+K^−$, $K^+ K^−$, and $\pi^+ \pi^−$, and, for the first time, in the four-body final states $K^+\pi^-\pi^+\pi^-$, $\pi^+K^−\pi^+\pi^−$, and $\pi^+\pi^−\pi^+\pi^−$. First observations of the decays $B^0 \to D(\pi^+K^−)K^{∗0}$ and $B^0 \to D(\pi^+\pi^−\pi^+\pi^−)K^{∗0}$ are obtained, and a set of observables comprising yield ratios and asymmetries is studied. The second measurement studies $D$-meson decays to the three-body final states $K_S^0\pi^+\pi^−$ and $K_S^0K^+K^−$ in a binned Dalitz plot analysis using 9 fb$^{-1}$ of data. The CP observables from both measurements are interpreted together to determine the CP-violating weak phase $\gamma = (77^{+8}_{-9})$◦. This is the world's most precise determination using only $B^0$-meson decays and is in agreement with the prediction of the Standard Model. The world's best measurements of the hadronic parameters $r_{B^0} = 0.258^{+0.022}_{-0.023}$ and $\delta_{B^0} = (200 \pm 8)$◦ are also presented.