The two-body hadronic decays of $B$ mesons into pseudoscalar and axial-vector mesons are studied within the framework of QCD factorization. The light cone distribution amplitudes (LCDAs) for ${}^{3}P_1$ and ${}^{1}P_1$ axial-vector mesons have been evaluated using the QCD sum rule method. Owing to the $G$-parity, the chiral-even two-parton light cone distribution amplitudes of the ${}^{3}P_1$ (${}^{1}P_1$) mesons are symmetric (antisymmetric) under the exchange of quark and antiquark momentum fractions in the SU(3) limit. For chiral-odd LCDAs, it is the other way around. The main results are the following: (i) The predicted rates for $a_1^{\pm }(1260){\pi }^{\mp }$, $b_1^{\pm }(1235){\pi }^{\mp }$, $b_1^0(1235){\pi }^{-}$, $a_1^{+}{K}^{-}$, and $b_1^{+}{K}^{-}$ modes are in good agreement with the data. However, the naively expected ratios $\mathcal{B}(B^{-}\to a_1^0{\pi }^{-})/\mathcal{B}({\overline{B}}^0\to a_1^{+}{\pi }^{-})\lesssim 1$, $\mathcal{B}(B^{-}\to a_1^{-}{\pi }^0)/\mathcal{B}({\overline{B}}^0\to a_1^{-}{\pi }^{+})\sim \frac{1}{2}$, and $\mathcal{B}(B^{-}\to b_1^0{K}^{-})/\mathcal{B}({\overline{B}}^0\to b_1^{+}{K}^{-})\sim \frac{1}{2}$ are not borne out by experiment. This should be clarified by the improved measurements of these decays. (ii) Since the $\overline{B}\to b_{1}K$ decays receive sizable annihilation contributions, their rates are sensitive to the interference between penguin and annihilation terms. The measurement of $\mathcal{B}({\overline{B}}^0\to b_1^{+}{K}^{-})$ implies a destructive interference which in turn indicates that the form factors for $B\to b_1$ and $B\to a_1$ transitions are of opposite signs. (iii) Sizable power corrections such as weak annihilation are needed to account for the observed rates of the penguin-dominated modes $K_1^{-}(1270){\pi }^{+}$ and $K_1^{-}(1400){\pi }^{+}$. (iv) The decays $B\to K_1\overline{K}$ with $K_1=K_1(1270)$, $K_1(1400)$ are in general quite suppressed, of order ${10}^{-7}–{10}^{-8}$, except for ${\overline{B}}^0\to {\overline{K}}_1^0(1270)K^0$ which can have a branching ratio of order $2.3\times {10}^{-6}$. The decay modes $K_1^{-}{K}^{+}$ and $K_1^{+}{K}^{-}$ are of particular interest as they proceed only through weak annihilation. (v) The mixing-induced parameter $S$ is predicted to be negative in the decays $B^0\to a_1^{\pm }{\pi }^{\mp }$, while it is positive experimentally. This may call for a larger unitarity angle $\gamma \gtrsim 80°$. (vi) Branching ratios for the decays $B\to f_1\pi$, $f_{1}K$, $h_1\pi$ and $h_{1}K$ with $f_1=f_1(1285)$, $f_1(1420)$ and $h_1=h_1(1170)$, $h_1(1380)$ are generally of order ${10}^{-6}$ except for the color-suppressed modes $f_1{\pi }^0$ and $h_1{\pi }^0$ which are suppressed by 1 to 2 orders of magnitude. Measurements of the ratios $\mathcal{B}(B^{-}\to h_1(1380){\pi }^{-})/\mathcal{B}(B^{-}\to h_1(1170){\pi }^{-})$ and $\mathcal{B}(\overline{B}\to f_1(1420)\overline{K})/\mathcal{B}(\overline{B}\to f_1(1285)\overline{K})$ will help determine the mixing angles ${\theta }_{{}^{1}P_1}$ and ${\theta }_{{}^{3}P_1}$, respectively.

• Received 4 September 2007

DOI:https://doi.org/10.1103/PhysRevD.76.114020