Spectator scattering and annihilation contributions as a solution to the $\pi K$ and $\pi \pi$ puzzles within QCD factorization approach
Spectator scattering and annihilation contributions as a solution to the $\pi K$ and $\pi \pi$ puzzles within QCD factorization approach
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DOI：
10.1103/physrevd.90.054019
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发表时间：
2014-09
影响因子：
5
通讯作者：
Qin Chang;Junfeng Sun;Yueling Yang;Xiaonan Li
中科院分区：
文献类型：
--
作者：
Qin Chang;Junfeng Sun;Yueling Yang;Xiaonan Li
纯湮灭的大分支比 $\bar{B}_s^0$ $\to$ $\pi^+ \pi^-$ 和 $\bar{B}_d^0$ $\to$ $K^+ K^-$ 最近由CDF和LHCb合作报道的衰变，以及所谓的 ${\pi}K$ 和 ${\pi}{\pi}$ 谜题表明，观众散射和湮灭对企鹅主导、颜色抑制树主导和纯湮灭非轻子的贡献是重要的 $B$ 衰变。结合现有的实验数据 $B_{u,d}$ ${\to}$ $\pi \pi$， ${\pi}K$ 和 $K \bar{K}$ 衰减，我们对观察者散射和湮灭参数做一个全局拟合 $X_H({\rho}_H$， ${\phi}_H)$， $X_A^i({\rho}_A^{i},{\phi}_A^{i})$ 和 $X_A^f({\rho}_A^{f},{\phi}_A^{f})$，分别在三种不同的情况下，用于参数化QCD分解框架内旁观者散射、不可分解和可分解湮灭拓扑振幅的端点奇异性。在情形二中，我们得到 $({\rho}_A^{i},{\phi}_A^{i}[^{\circ}])=(2.88^{+1.52}_{-1.30},-103^{+33}_{-40})$ 和 $({\rho}_A^{f},{\phi}_A^{f}[^{\circ}])=(1.21^{+0.22}_{-0.25},-40^{+12}_{-8})$ 在… $68\%$ 置信水平，这主要是解决所要求的 ${\pi}K$ 疑惑并确认这个假设 $X_A^i\neq X_A^f$． 此外，相应地， $B$-介子波函数参数 $\lambda_B$ 是不是也适合 $0.18^{+0.11}_{-0.08}\, MeV$这对解决这两个问题都起着重要作用 ${\pi}K$ 和 $\pi\pi$ 拼图。的QCDF结果 $B_{u,d}$ $\to$ $\pi \pi$， $\pi K$ 和 $K \bar{K}$ 衰变与实验测量结果非常吻合。期望有更多的实验和理论努力来理解旁观者散射和湮灭贡献的潜在QCD动力学。
The large branching ratios for pure annihilation $\bar{B}_s^0$ $\to$ $\pi^+ \pi^-$ and $\bar{B}_d^0$ $\to$ $K^+ K^-$ decays reported by CDF and LHCb collaborations recently and the so-called ${\pi}K$ and ${\pi}{\pi}$ puzzles indicate that spectator scattering and annihilation contributions are important to the penguin-dominated, color-suppressed tree dominated, and pure annihilation nonleptonic $B$ decays. Combining the available experimental data for $B_{u,d}$ ${\to}$ $\pi \pi$, ${\pi}K$ and $K \bar{K}$ decays, we do a global fit on the spectator scattering and annihilation parameters $X_H({\rho}_H$, ${\phi}_H)$, $X_A^i({\rho}_A^{i},{\phi}_A^{i})$ and $X_A^f({\rho}_A^{f},{\phi}_A^{f})$, which are used to parameterize the endpoint singularity in amplitudes of spectator scattering, nonfactorizable and factorizable annihilation topologies within the QCD factorization framework, in three scenarios for different purpose. Numerically, in scenario II, we get $({\rho}_A^{i},{\phi}_A^{i}[^{\circ}])=(2.88^{+1.52}_{-1.30},-103^{+33}_{-40})$ and $({\rho}_A^{f},{\phi}_A^{f}[^{\circ}])=(1.21^{+0.22}_{-0.25},-40^{+12}_{-8})$ at the $68\%$ confidence level, which are mainly demanded by resolving ${\pi}K$ puzzle and confirm the presupposition that $X_A^i\neq X_A^f$. In addition, correspondingly, the $B$-meson wave function parameter $\lambda_B$ is also fitted to be $0.18^{+0.11}_{-0.08}\, MeV$, which plays an important role for resolving both ${\pi}K$ and $\pi\pi$ puzzles. With the fitted parameters, the QCDF results for observables of $B_{u,d}$ $\to$ $\pi \pi$, $\pi K$ and $K \bar{K}$ decays are in good agreement with experimental measurements. Much more experimental and theoretical efforts are expected to understand the underlying QCD dynamics of spectator scattering and annihilation contributions.