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arXiv 1003.3348hep-ph
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对$\bar{B_{d}^0} \to π^0 D^{0}$的不可因式分解贡献

Non-factorizable contribtion to $\bar{B_{d}^0} \to π^0 D^{0}$

Lars E. Leganger, Jan O. Eeg

摘要:

$B \to π\, D $类型的衰变模式在动力学上是不同的。对于$\bar{B_{d}^0} \to π^- D^{+} $的情况,存在占主导地位的实质性因子分解贡献。相反,衰减模式$\bar{B_{d}^0} \to π^0 D^{0} $具有小的因子分解贡献,与非常小的威尔逊系数组合成比例。本文计算了$b$ -夸克和$c$ -夸克在重夸克极限下单圈水平上的Wilson系数。我们还强调,对于衰减模式$\bar{B_{d}^0} \to π^0 D^{0}$有一个相当大的不可因式分解的贡献,由于长距离的相互作用,占主导地位的振幅。在我们的框架内,我们估计这种衰变模式的分支比,它使用重夸克的限制,无论是$b$ -和$c$ -夸克。此外,我们治疗高能光($u,d,s$)夸克内的大能量有效理论的一个变体,并结合这与手征夸克模型的一个新的扩展。对于合理的值的模型依赖的参数,我们的模型可以占至少3/4的振幅需要解释的实验分支比$\simeq 2.6 \times 10^{-4}$。

英文摘要:

The decay modes of the type $B \to π\, D $ are dynamically different. For the case $\bar{B_{d}^0} \to π^- D^{+} $ there is a substantial factorized contribution which dominates. In contrast, the decay mode $\bar{B_{d}^0} \to π^0 D^{0} $ has a small factorized contribution, being proportional to a very small Wilson coefficient combination. In this paper we calculate the relevant Wilson coefficients at one loop level in the heavy quark limits, both for the $b$-quark and the $c$-quark. We also emphasize that for the decay mode $\bar{B_{d}^0} \to π^0 D^{0}$ there is a sizeable non-factorizable contribution due long distance interactions, which dominate the amplitude. We estimate the branching ratio for this decay mode within our framework, which uses the heavy quark limits, both for the $b$- and the $c$-quarks. In addition, we treat energetic light ($u,d,s$) quarks within a variant of Large Energy Effective Theory and combine this with a new extension of chiral quark models. For reasonable values of the model dependent parameters of our model can account for at least 3/4 of the amplitude needed to explain the experimental branching ratio $\simeq 2.6 \times 10^{-4}$.

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