Hadronic charmless<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>A</mml:mi><mml:mi>P</mml:mi></mml:math> (2007)

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 ${a}_{1}^{\ifmmode\pm\else\textpm\fi{}}(1260){\ensuremath{\pi}}^{\ensuremath{\mp}}$, ${b}_{1}^{\ifmmode\pm\else\textpm\fi{}}(1235){\ensuremath{\pi}}^{\ensuremath{\mp}}$, ${b}_{1}^{0}(1235){\ensuremath{\pi}}^{\ensuremath{-}}$, ${a}_{1}^{+}{K}^{\ensuremath{-}}$, and ${b}_{1}^{+}{K}^{\ensuremath{-}}$ modes are in good agreement with the data. However, the naively expected ratios $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{a}_{1}^{0}{\ensuremath{\pi}}^{\ensuremath{-}})/\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{a}_{1}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})\ensuremath{\lesssim}1$, $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{a}_{1}^{\ensuremath{-}}{\ensuremath{\pi}}^{0})/\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{a}_{1}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})\ensuremath{\sim}\frac{1}{2}$, and $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{b}_{1}^{0}{K}^{\ensuremath{-}})/\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{b}_{1}^{+}{K}^{\ensuremath{-}})\ensuremath{\sim}\frac{1}{2}$ are not borne out by experiment. This should be clarified by the improved measurements of these decays. (ii) Since the $\overline{B}\ensuremath{\rightarrow}{b}_{1}K$ decays receive sizable annihilation contributions, their rates are sensitive to the interference between penguin and annihilation terms. The measurement of $\mathcal{B}({\overline{B}}^{0}\ensuremath{\rightarrow}{b}_{1}^{+}{K}^{\ensuremath{-}})$ implies a destructive interference which in turn indicates that the form factors for $B\ensuremath{\rightarrow}{b}_{1}$ and $B\ensuremath{\rightarrow}{a}_{1}$ 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 ${K}_{1}^{\ensuremath{-}}(1270){\ensuremath{\pi}}^{+}$ and ${K}_{1}^{\ensuremath{-}}(1400){\ensuremath{\pi}}^{+}$. (iv) The decays $B\ensuremath{\rightarrow}{K}_{1}\overline{K}$ with ${K}_{1}={K}_{1}(1270)$, ${K}_{1}(1400)$ are in general quite suppressed, of order ${10}^{\ensuremath{-}7}--{10}^{\ensuremath{-}8}$, except for ${\overline{B}}^{0}\ensuremath{\rightarrow}{\overline{K}}_{1}^{0}(1270){K}^{0}$ which can have a branching ratio of order $2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. The decay modes ${K}_{1}^{\ensuremath{-}}{K}^{+}$ and ${K}_{1}^{+}{K}^{\ensuremath{-}}$ 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 ${B}^{0}\ensuremath{\rightarrow}{a}_{1}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{\ensuremath{\mp}}$, while it is positive experimentally. This may call for a larger unitarity angle $\ensuremath{\gamma}\ensuremath{\gtrsim}80\ifmmode^\circ\else\textdegree\fi{}$. (vi) Branching ratios for the decays $B\ensuremath{\rightarrow}{f}_{1}\ensuremath{\pi}$, ${f}_{1}K$, ${h}_{1}\ensuremath{\pi}$ 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 ${10}^{\ensuremath{-}6}$ except for the color-suppressed modes ${f}_{1}{\ensuremath{\pi}}^{0}$ and ${h}_{1}{\ensuremath{\pi}}^{0}$ which are suppressed by 1 to 2 orders of magnitude. Measurements of the ratios $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}_{1}(1380){\ensuremath{\pi}}^{\ensuremath{-}})/\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}_{1}(1170){\ensuremath{\pi}}^{\ensuremath{-}})$ and $\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{f}_{1}(1420)\overline{K})/\mathcal{B}(\overline{B}\ensuremath{\rightarrow}{f}_{1}(1285)\overline{K})$ will help determine the mixing angles ${\ensuremath{\theta}}_{^{1}P_{1}}$ and ${\ensuremath{\theta}}_{^{3}P_{1}}$, respectively.