Polarizations in B -> VV decays

Abstract

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 $B^0\to (D_s^{\ast +},D^{\ast +},{\rho }^{+})D^{\ast -}$ and $B^{+}\to (D_s^{\ast +},D^{\ast +},{\rho }^{+}){\rho }^0$ modes increase as the masses of the mesons $D_s^{\ast +},D^{\ast +},{\rho }^{+}$ emitted from the weak vertex decrease. The subleading finite-mass or finite-energy corrections modify these simple estimates only slightly. Our predictions for the $B\to D_{(s)}^{\ast }{D}^{\ast }$ polarization fractions derived in the perturbative QCD framework, especially $R_L\sim 1$ for $B^0\to {\bar{D}}^{\ast 0}{D}^{\ast 0}$ governed by nonfactorizable $W$-exchange amplitudes, can be confronted with future data. For penguin-dominated modes, such as $B\to \rho (\omega )K^{\ast }$, 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 $B\to \varphi K^{\ast }$ polarization data, none of which are satisfactory.

Comments: 26 pages, 4 figures; corrected typos, version to appear in Phys. Rev. D