  In this paper, we examine B -> VT decays (V is a vector and T is a tensor
meson), whose final-state particles can have transverse or longitudinal
polarization. Measurements have been made of B -> \phi K_2^*, and it is found
that fT/fL is small, where fT (fL) is the fraction of transverse (longitudinal)
decays. We find that the standard model (SM) naively predicts that fT/fL << 1.
The two extensions of the naive SM which have been proposed to explain the
large fT/fL in B -> \phi K^* -- penguin annihilation and rescattering -- make
no firm predictions for the polarization in B -> \phi K_2^*. The two
new-physics scenarios, which explain the data in B -> \pi K and the \phi (\rho)
K^* polarization measurements, can reproduce the fT/fL data in B -> \phi K_2^*
only if the B -> T form factors obey a certain hierarchy. Finally, we present
the general angular analysis which can be used to get helicity information
using two- and three-body decays.
