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

Abstract

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 $\rho (\omega ,\varphi )$. 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 ${\bar{B}}^0\to a_1^0{\rho }^0(\omega )$, 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 $B^{-}\to b_1^0{\rho }^{-}$, other $B\to b_1\rho (\omega )$ decays have smaller branching ratios, at the order of $10^{-6}$. (c) The decays $B\to a_1(b_1)\varphi$ 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 $B^{-}\to a_1^0{\rho }^{-},b_1^0{\rho }^{-}$ and ${\bar{B}}^0\to b_1^0{\rho }^0,b_1^0\omega$, 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.

Comments: 15pages, 4 figures