Branching Ratios and CP Asymmetries of B \to a_1(1260) \pi and a_1(1260) K Decays

We present the studies of the decays $B\to a_1(1260)\pi$ and $a_1(1260)K$ within the framework of QCD factorization. Due to the G-parity, unlike the vector meson, the chiral-odd two-parton light-cone distribution amplitudes of the $a_1$ are antisymmetric under the exchange of quark and anti-quark momentum fractions in the SU(2) limit. The branching ratios for $a_1\pi$ modes are sensitive to tree–penguin interference. The resultant ${\cal B}(B^0 \to a_1^\pm \pi^\mp)$ are in good agreement with the data. However, using the current Cabibbo–Kobayashi–Maskawa angles, $\beta ={22.0}^{\circ }$ and $\gamma ={59.0}^{\circ }$, our results for the mixing-induced parameter $S$ and ${\alpha }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ differ from the measurements of the time-dependent CP asymmetries in the decay $B^0\to a_1^{\pm }{\pi }^{\mp }$ at about the $3.7\sigma$ level. This puzzle may be resolved by using a larger $\gamma \gtrsim {80}^{\circ }$. For $a_{1}K$ modes, the annihilation topologies give sizable contributions and are sensitive to the first Gegenbauer moment of the leading-twist tensor (chiral-odd) distribution amplitude of the $a_1$ meson. The $B\to a_{1}K$ amplitudes resemble the corresponding $B\to \pi K$ ones very much. Taking the ratios of corresponding CP-averaged $a_{1}K$ and $\pi K$ branching ratios, we can extract information relevant to the electroweak penguins and annihilations. The existence of new-physics in the electroweak penguin sector and final state interactions during decays can thus be explored.