Measurement of CP observables in the process B ⁰ → DK ^*0 with two- and four-body D decays

Measurements of CP observables in B⁰ → DK^∗0 decays are presented, where D represents a superposition of D⁰ and D¯ states. The D meson is reconstructed in the two-body final states K⁺π⁻, π⁺K⁻, K⁺K⁻ and π⁺π⁻, and, for the first time, in the fourbody final states K⁺π⁻π⁺π⁻, π⁺K⁻π⁺π⁻ and π⁺π⁻π⁺π⁻. 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 fb⁻¹ collected with the LHCb detector at centre-of-mass energies of s=7,8 and 13 TeV, respectively. First observations of the decays B⁰ → D(π⁺K⁻)K^∗0 and B⁰ → D(π⁺π⁻π⁺π⁻)K^∗0 are obtained. The measured observables are interpreted in terms of the CP -violating weak phase γ. [Figure not available: see fulltext.]