Amplitude analysis of the B(s)0→^{K∗0 K¯∗0} decays and measurement of the branching fraction of the B→ K^{∗ 0}K¯ ^{∗ 0} decay

The B→ K^{∗ 0}K¯ ^{∗ 0} and Bs0→K∗0K¯∗0 decays are studied using proton-proton collision data corresponding to an integrated luminosity of 3 fb⁻¹. An untagged and timeintegrated amplitude analysis of B_(s) ⁰ → (K⁺π⁻)(K⁻π⁺) decays in two-body invariant mass regions of 150 MeV/c² around the K^∗0 mass is performed. A stronger longitudinal polarisation fraction in the B→ K^{∗ 0}K¯ ^{∗ 0} decay, f_L = 0.724 ± 0.051 (stat) ± 0.016 (syst), is observed as compared to f_L = 0.240 ± 0.031 (stat) ± 0.025 (syst) in the Bs0→K∗0K¯∗0 decay. The ratio of branching fractions of the two decays is measured and used to determine ℬ(B0→K∗0K¯∗0)=(8.0±0.9(stat)±0.4(syst))×10−7.