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

Abstract

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 $\mathcal{B}(B^0\to a_1^{\pm }{\pi }^{\mp })$ 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 ${\alpha }_{\mathrm{eff}}$ 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.

Comments: 20 pages, 1 figure, 4 tables, typos corrected, some discussions added, version to appear in PRD