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We measure the following branching fractions in units of 10^{-6}: B (B+ --> rho0 K*+) = 3.6 +/- 1.7 +/- 0.8 (< 6.1), B (B+ --> rho+ K*0) = 9.6 +/- 1.7 +/- 1.5, B (B0 --> rho- K*+) = 5.4 +/- 3.6 +/- 1.6 (< 12.0), B (B0 --> rho0 K*0) = 5.6 +/- 0.9 +/- 1.3, B (B+ --> f0(980) K*+) = 5.2 +/- 1.2 +/- 0.5, and B (B0 --> f0(980) K*0) = 2.6 +/- 0.6 +/- 0.9 (< 4.3). 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Aubert, et al, The BABAR Collaboration","submitted_at":"2006-07-25T20:23:40Z","abstract_excerpt":"We report searches for B-meson decays to the charmless final states rho K* and f0(980) K* with a sample of 232 million BBbar pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We measure the following branching fractions in units of 10^{-6}: B (B+ --> rho0 K*+) = 3.6 +/- 1.7 +/- 0.8 (< 6.1), B (B+ --> rho+ K*0) = 9.6 +/- 1.7 +/- 1.5, B (B0 --> rho- K*+) = 5.4 +/- 3.6 +/- 1.6 (< 12.0), B (B0 --> rho0 K*0) = 5.6 +/- 0.9 +/- 1.3, B (B+ --> f0(980) K*+) = 5.2 +/- 1.2 +/- 0.5, and B (B0 --> f0(980) K*0) = 2.6 +/- 0.6 +/- 0.9 (< 4.3). 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