Measurement of the branching fractions and longitudinal polarizations of B ( s ) 0 → K * 0 K ¯ * 0 decays

A time- and flavor-integrated amplitude analysis of B 0 and B s 0 decays to the ( K + π − ) ( K − π + ) final state in the K * ( 892 ) 0 K ¯ * ( 892 ) 0 region is presented, using p p collision data recorded with the LHCb detector in 2011–2018, corresponding to an integrated luminosity of 9 fb − 1 . The branching fractions of the B 0 and B s 0 decays are measured relative to the B 0 → D − π + and B s 0 → D s − π + modes, respectively. The corresponding longitudinal polarization fractions are found to be f L d = 0.600 ± 0.022 ± 0.017 and f L s = 0.159 ± 0.010 ± 0.007 , where the uncertainties are statistical and systematic, respectively. The theory-motivated ratio of the squared B s 0 to B 0 longitudinally polarized decay amplitudes is found to be L K * 0 K ¯ * 0 = 4.92 ± 0.55 ± 0.48 ± 0.02 ± 0.10 , where the uncertainties are statistical, systematic, due to uncertainty of external mass and lifetime measurements, and due to knowledge of the fragmentation fraction ratio, respectively. This confirms the previously reported tension between experimental determinations and theoretical predictions of longitudinal polarization in B → V V decays at the level of 4.4 standard deviations.