Amplitude analysis of the B s 0 → K ∗ 0 K ¯ ∗ 0 $$ {B}_{(s)}^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ decays and measurement of the branching fraction of the B 0 → K ∗ 0 K ¯ ∗ 0 $$ {B}^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ decay

Abstract The B 0 → K ∗ 0 K ¯ ∗ 0 $$ {B}^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ and B s 0 → K ∗ 0 K ¯ ∗ 0 $$ {B}_s^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ 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/c 2 around the K ∗0 mass is performed. A stronger longitudinal polarisation fraction in the B 0 → K ∗ 0 K ¯ ∗ 0 $$ {B}^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ 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 B s 0 → K ∗ 0 K ¯ ∗ 0 $$ {B}_s^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0} $$ decay. The ratio of branching fractions of the two decays is measured and used to determine ℬ B 0 → K ∗ 0 K ¯ ∗ 0 = 8.0 ± 0.9 stat ± 0.4 syst × 10 − 7 $$ \mathrm{\mathcal{B}}\left({B}^0\to {K}^{\ast 0}{\overline{K}}^{\ast 0}\right)=\left(8.0\pm 0.9\left(\mathrm{stat}\right)\pm 0.4\left(\mathrm{syst}\right)\right)\times {10}^{-7} $$ .