Branching Ratios and Polarization in B-> VV,VA,AA Decays

Abstract

We present a detailed study of charmless two-body B decays into final states involving two vector mesons (VV) or two axial-vector mesons (AA) or one vector and one axial-vector meson (VA), within the framework of QCD factorization, where $A$ is either a ${}^3{P}_1$ or ${}^1{P}_1$ axial-vector meson. The main results are as follows. (i) In the presence of NLO nonfactorizable corrections, effective Wilson coefficients $a_i^h$ are helicity dependent. For some penguin-dominated modes, the constructive (destructive) interference in the negative-helicity (longitudinal-helicity) amplitude of the $B\to VV$ decay will render the former comparable to the latter and push up the transverse polarization. (ii) In QCD factorization, the transverse polarization fraction can be large for penguin-dominated charmless $VV$ modes by allowing for sizable penguin annihilation contributions. (iii) Using the measured ${\bar{K}}^{\ast 0}{\rho }^{-}$ channel as an input, we predict the branching ratios and polarization fractions for other $\text{ov}B\to {\bar{K}}^{\ast }\rho$ decays. (iv) The smallness of the axial-vector decay constant of the ${}^1{P}_1$ axial vector meson can be tested by measuring various $b_1\rho$ modes to see if $\Gamma ({\bar{B}}^0\to b_1^{-}{\rho }^{+})\ll \Gamma ({\bar{B}}^0\to b_1^{+}{\rho }^{-})$ and $\Gamma (B^{-}\to b_1^{-}{\rho }^0)\ll \Gamma (B^{-}\to b_1^0{\rho }^{-})$. (v) For the penguin-dominated modes $a_1{K}^{\ast }$ and $b_1{K}^{\ast }$, it is found that the former are dominated by transverse polarization amplitudes, whereas the latter are governed by longitudinal polarization states.

Comments: 58 pages, 2 figures. The charm quark mass in the penguin loop corrections is changed to the pole mass one. Fig. 1 and all the numerical results in Tables IX-XI and the content are revised accordingly. Version to appear in PRD