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

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

2007-05-28

arxiv.org/abs/0705.4029v2

Phys.Rev.D76:094002,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevD.76.094002

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 $\alpha_{\rm eff}$ 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.

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