Calculations of branching ratios and longitudinal polarization fractions in B0 → K*0K̄*0 and B0s → K*0K̄*0 decays.

In this paper, I have investigated the two-body pure penguin decays of B 0 → K * 0 K ¯ * 0 and B s 0 → K * 0 K ¯ * 0 , that these were collected with the LHCb detector, and the branching fractions were measured to be B (B 0 → K * 0 K ¯ * 0) = (8.0 ± 0.9 ± 0.4) × 10 − 7 and B (B s 0 → K * 0 K ¯ * 0) = (10.8 ± 2.1 ± 1.5) × 10 − 6 . I have studied these decay modes within the framework of the factorization approach by using three different energy scales; while in calculating the amplitude of these decays, the multiplications of four vectors of the polarization vectors, such as (ε K ¯ * 0 · ε K * 0 ) , (ε K ¯ * 0 · p B (s) ) , and (ε K * 0 · p B (s) ) appear. These parameters have been calculated based on helicity amplitudes (A 0 , A + , A −) ; the results obtained for branching fractions in the μ = mb/2 scale are B (B 0 → K * 0 K ¯ * 0) = (7.1 ± 1.3) × 10 − 7 and B (B s 0 → K * 0 K ¯ * 0) = (10.2 ± 1.9) × 10 − 6 . I have also estimated the fractions of longitudinal polarizations in B 0 → K * 0 K ¯ * 0 and B s 0 → K * 0 K ¯ * 0 decay modes by considering the transverse amplitudes (A ⊥ , A ∥) ; at the μ = mb/2 scale the results are obtained to be f L (B 0 → K * 0 K ¯ * 0) = 0.519 ± 0.067 and f L (B s 0 → K * 0 K ¯ * 0) = 0.419 ± 0.054 , which are comparable to the experimental results, 0.724 ± 0.051 ± 0.016 and 0.694 ± 0.016 ± 0.012, respectively, reported by the LHCb collaboration. [ABSTRACT FROM AUTHOR]