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Polarizations in B -> VV decays

We demonstrate that the polarization fractions of most tree-dominated $B\to VV$ decays can be simply understood by means of kinematics in the heavy-quark or large-energy limit. For example, the longitudinal polarization fractions $R_L$ of the $B^0\to (D_s^{*+}, D^{*+}, ρ^+)D^{*-}$ and $B^+\to (D_s^{*+}, D^{*+}, ρ^+)ρ^0$ modes increase as the masses of the mesons $D_s^{*+}, D^{*+}, ρ^+$ emitted from the weak vertex decrease. The subleading finite-mass or finite-energy corrections modify these simple estimates only slightly. Our predictions for the $B\to D_{(s)}^* D^*$ polarization fractions derived in the perturbative QCD framework, especially $R_L\sim 1$ for $B^0\to {\bar D}^{*0} D^{*0}$ governed by nonfactorizable $W$-exchange amplitudes, can be confronted with future data. For penguin-dominated modes, such as $B\toρ(ω) K^*$, the polarization fractions can be understood by the annihilation effect from the $(S-P)(S+P)$ operators, plus the interference with a small tree amplitude. At last, we comment on the various mechanism proposed in the literature to explain the abnormal $B\to ϕK^*$ polarization data, none of which are satisfactory.