$B\to \varphi K^{*}$ ($\overline{b}\to \overline{s}$) 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, $f_T$, and the fraction of longitudinal decays, $f_L$, are roughly equal: $f_T/f_L\simeq 1$, in opposition to the naive expectation that $f_T\ll f_L$. 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 $f_T/f_L$ in $\overline{b}\to \overline{d}$ decays. In $B\to \rho \rho$ decays, only $B_d^0\to {\rho }^0{\rho }^0$ can possibly exhibit a large $f_T/f_L$. In $B$ decays related by U-spin, we find two promising possibilities: (i) $B^{+}\to K^{*0}{\rho }^{+}$ ($\overline{b}\to \overline{s}$) and $B^{+}\to {\overline{K}}^{*0}{K}^{*+}$ ($\overline{b}\to \overline{d}$) and (ii) $B_s\to K^{*0}{\overline{K}}^{*0}$ ($\overline{b}\to \overline{s}$) and $B_d^0\to {\overline{K}}^{*0}{K}^{*0}$ ($\overline{b}\to \overline{d}$). The measurement of $f_T/f_L$ 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 $B_d^0\to {\overline{K}}^{*0}{K}^{*0}$.

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