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arXiv 1012.4323hep-ph
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关于颜色抑制对$ \bar{B_{d}^0} \rightarrow的影响\，π^0 π^{0}

On the color suppressed contribution to $\bar{B_{d}^0} \rightarrow \, π^0 π^{0}

Jan O. Eeg, Teresa Palmer

备注：
The submitted Latex version correspond to 23 pages in ps-version and contains 4 figures
发表信息：
Phys.Rev.D83:054016,2011
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摘要：

$B \rightarrow π\, π$类型的衰变模式在动力学上是不同的。对于$\bar{B_{d}^0} \rightarrow \, π^+ π^- $的情况，存在占主导地位的实质性因子分解贡献。相反，衰减模式$\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $具有小的因子分解贡献，与小的威尔逊系数组合成比例。然而，对于衰减模式$\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $，由于软（长距离）相互作用，占主导地位的幅度，有相当大的不可因式分解（颜色抑制）的贡献。我们估计了$b$ -夸克重夸克极限下$\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $模的分支比。为了估计色抑制的贡献，我们处理高能光（$u,d,s$）夸克的大能量有效理论的一个变体结合最近的手征夸克模型的扩展模型依赖的胶子凝聚。我们发现，我们计算的颜色抑制振幅被抑制的$Λ_{QCD}/m_b$阶的因子相对于可因子化的振幅，因为它应该根据QCD因子化。此外，对于组分夸克质量和胶子凝聚的合理值，计算的$\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $不可因式分解振幅可以很容易地适应实验值。不幸的是，颜色抑制幅度对这些模型相关参数的值非常敏感。因此，为了获得与$\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $的实验结果相一致的振幅，微调是必要的。一个可能的联系，三角形异常进行了讨论。

英文摘要：

The decay modes of the type $B \rightarrow π\, π$ are dynamically different. For the case $\bar{B_{d}^0} \rightarrow \, π^+ π^- $ there is a substantial factorized contribution which dominates. In contrast, the decay mode $\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $ has a small factorized contribution, being proportional to a small Wilson coefficient combination. However, for the decay mode $\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $ there is a sizeable nonfactorizable (color suppressed) contribution due to soft (long distance) interactions, which dominate the amplitude. We estimate the branching ratio for the mode $\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $ in the heavy quark limit for the $b$- quark. In order to estimate color suppressed contributions we treat the energetic light ($u,d,s$) quark within a variant of Large Energy Effective Theory combined with a recent extension of chiral quark models in terms of model- dependent gluon condensates. We find that our calculated color suppressed amplitude is suppressed by a factor of order $Λ_{QCD}/m_b$ with respect to the factorizable amplitude, as it should according to QCD-factorization. Further, for reasonable values of the constituent quark mass and the gluon condensate, the calculated nonfactorizable amplitude for $\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $ can easily accomodate the experimental value. Unfortunately, the color suppressed amplitude is very sensitive to the values of these model dependent parameters. Therefore fine-tuning is necessary in order to obtain an amplitude compatible with the experimental result for $\bar{B_{d}^0} \rightarrow \, π^0 π^{0} $. A possible link to the triangle anomaly is discussed.

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