We study the nonleptonic decays of $B\to PP$ in the modified perturbative QCD approach, where $P$ stands for pseudoscalar mesons. Transverse momenta of partons and the Sudakov factor are included, which help to suppress the contributions of soft interactions. The wave function of the $B$ meson obtained from the relativistic potential model is used, and then the contributions in the infrared region cannot be suppressed completely. So a soft cutoff scale and soft form factors are introduced. The contributions with the scale higher than the soft cutoff scale are calculated with perturbative QCD, while the contributions lower than the cutoff scale are replaced by the soft form factors. To explain experimental data, we find that contributions of color-octet operators for the quark-antiquarks in the mesons in the final state need to be considered. The contributions of the color-octet operators are parametrized by a few parameters with the help of SU(3) flavor symmetry and symmetry breaking. These parameters for color-octet contributions are universal for all the nonleptonic decay modes of the $B$ meson, where the mesons in the final state belong to the same flavor SU(3) nonet. Both the branching ratios and $CP$ violations are studied. We find that the theoretical calculation can well explain the experimental data of $B$ factories.

中文翻译：

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改进的微扰 QCD 方法中 B→PP 衰变的研究


我们研究非轻子衰变 $B\to PP$ 在改进的微扰 QCD 方法中，其中 $P$ 代表赝标量介子。包括部分子的横向动量和苏达科夫因子，这有助于抑制软相互作用的贡献。的波函数 $B$ 采用相对论势模型得到的介子，无法完全抑制红外区的贡献。因此引入了软截止尺度和软形状因子。高于软截止尺度的贡献用微扰QCD计算，而低于截止尺度的贡献则用软形状因子代替。为了解释实验数据，我们发现需要考虑最终状态下介子中夸克-反夸克的颜色八位组算子的贡献。借助 SU(3) 风味对称性和对称性破缺，可以通过一些参数对颜色八位组运算符的贡献进行参数化。这些颜色八位组贡献的参数对于所有非轻子衰变模式都是通用的。 $B$ 介子，其中最终状态的介子属于相同的味道 SU(3) nonet。 $B$ 或支化比和 $CP$ 违规行为受到研究。我们发现理论计算可以很好地解释B厂的实验数据。