Branching Ratio and Polarization of B \to   a_1(1260)(b_1(1235))\rho(\omega, \phi) Decays in the PQCD Approach
  Within the framework of perturbative QCD approach, we study the charmless two-body decays into final states involving one axial-vector (A), $a_1(1260)$ or $b_1(1235)$, and one vector (V), namely $\rho(\omega,\phi)$. Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) Except the decays $\bar B^0\to a^{0}_1\rho^0(\omega)$, other tree-dominated decays $B\to a_1\rho(\omega)$ have larger branching ratios, at the order of $10^{-5}$. (b)Except the decays $\bar B\to b^+_1\rho^-$ and $B^-\to b^0_1\rho^-$, other $B\to b_1\rho(\omega)$ decays have smaller branching ratios, at the order of $10^{-6}$. (c) The decays $B\to a_1(b_1) \phi$ are highly suppressed and have very small branching ratios, at the order of $10^{-9}$. (d) For the decays $\bar B^0 \to a_1^0\rho^0$ and $B^-\to b_1^-\rho^0$, their two transverse polarizations are larger than their longitudinal polarizations, which are about 43.3% and 44.9%, respectively. (d) The two transverse polarizations have near values in the decays $B\to a_1\rho(\omega)$, while have large differences in some of $B\to b_1\rho(\omega)$ decays. (e) For the decays $B^-\to a^{0}_1\rho^-, b^{0}_1\rho^-$ and $\bar B^0\to b^{0}_1\rho^0, b^{0}_1\omega$, where the transverse polarization fractions range from 4.7 to 7.5%, we calculate their direct CP-violating asymmetries with neglecting the transverse polarizations and find that those for two charged decays have smaller values, which are about 11.8% and -3.7%, respectively. 
Zhi-Qing Zhang
hep-ph