Measurements of branching fractions, polarizations, and direct CP-violation asymmetries in B --> rho K* and B --> f0(980) K* decays

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). The first error quoted is statistical, the second systematic, and the upper limits, in parentheses, are given at the 90% confidence level. For the statistically significant modes we also measure the fraction of longitudinal polarization and the charge asymmetry: f_L (B+ --> rho+ K*0) = 0.52 +/- 0.10 +/- 0.04, f_L (B0 --> rho0 K*0) = 0.57 +/- 0.09 +/- 0.08, A_CP (B+ --> rho+ K*0) = -0.01 +/- 0.16 +/- 0.02, A_CP (B0 --> rho0 K*0) = 0.09 +/- 0.19 +/- 0.02, A_CP (B+ --> f_0(980) K*+) = -0.34 +/- 0.21 +/- 0.03, and A_CP (B0 --> f_0(980) K*0) = -0.17 +/- 0.28 +/- 0.02.