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Within the framework of perturbative QCD approach, we study the charmlesstwo-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 thedecays constants and the light-cone distribution amplitudes for these mesonsderived from the QCD sum rule method, we find the following results: (a) Exceptthe 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 havevery 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 transversepolarizations are larger than their longitudinal polarizations, which are about43.3% and 44.9%, respectively. (d) The two transverse polarizations have nearvalues in the decays $B\to a_1\rho(\omega)$, while have large differences insome of $B\to b_1\rho(\omega)$ decays. (e) For the decays $B^-\toa^{0}_1\rho^-, b^{0}_1\rho^-$ 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%, wecalculate their direct CP-violating asymmetries with neglecting the transversepolarizations and find that those for two charged decays have smaller values,which are about 11.8% and -3.7%, respectively.

Branching Ratio and Polarization of B \to a_1(1260)(b_1(1235))\rho(\omega, \phi) Decays in the PQCD Approach