Measurement of $C!P$ observables in the process $B^0 to DK^{*0}$ with two- and four-body $D$ decays

Measurements of $C!P$ observables in $B^0 to DK^{*0}$ decays are presented, where $D$ represents a superposition of $D^0$ and $bar{D}^0$ states. The $D$ meson is 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 $pi^+pi^-pi^+pi^-$. The analysis uses a sample of neutral $B$ mesons produced in proton-proton collisions, corresponding to an integrated luminosity of 1.0, 2.0 and 1.8 $rm fb^{-1}$ collected with the LHCb detector at centre-of-mass energies of $sqrt{s} = $ 7, 8 and 13 TeV, respectively. 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. The measured observables are interpreted in terms of the $C!P$-violating weak phase $gamma$.