Testing explanations of the B→φK* polarization puzzle

B→φK* (b→s) is three separate decays, one for each polarization of the final-state vector mesons (one longitudinal, two transverse). It is observed that the fraction of transverse decays, fT, and the fraction of longitudinal decays, fL, are roughly equal: fT/fL≅1, in opposition to the naive expectation that fT<<fL. If one requires a single explanation of all polarization puzzles, two possibilities remain within the standard model: penguin annihilation and rescattering. In this paper we examine the predictions of these two explanations for fT/fL in b→d decays. In B→ρρ decays, only Bd0→ρ0ρ0 can possibly exhibit a large fT/fL. In B decays related by U-spin, we find two promising possibilities: (i) B+→K*0ρ+ (b→s) and B+→K*0K*+ (b→d) and (ii) Bs→K*0K*0 (b→s) and Bd0→K*0K*0 (b→d). The measurement of fT/fL in these pairs of decays will allow us to test penguin annihilation and rescattering. Finally, it is possible to distinguish penguin annihilation from rescattering by performing a time-dependent angular analysis of Bd0→K*0K*0