Charmless Hadronic Decays of B Mesons to a Pseudoscalar and a Tensor Meson

We study two-body charmless hadronic decays of $B$ mesons to a pseudoscalar meson ($P$) and a tensor meson ($T$) in the frameworks of both flavor SU(3) symmetry and generalized factorization. Certain ways to test validity of the generalized factorization are proposed, based on the flavor SU(3) analysis. We present a set of relations between a flavor SU(3) amplitude and a corresponding amplitude in the generalized factorization which bridge both approaches in $B \to PT$ decays. The branching ratios and CP asymmetries are calculated using the \emph{full} effective Hamiltonian including all the \emph{penguin} operators and the form factors obtained in the non-relativistic quark model of Isgur, Scora, Grinstein and Wise. We identify the decay modes in which the branching ratios and CP asymmetries are expected to be relatively large.