研究粒子物理世界和探索早期宇宙演化的一个必不可的内容就是$CP$破坏。$CP$破坏是粒子物理中弱相互作用的最基本也是最重要的性质之一。自1964年被发现以来，$CP$破坏备受科学家们的青睐。在标准模型的理论框架下，$CP$破坏中的弱相角来自于Cabibbo-Kobayashi-Maskawa (CKM) 矩阵元（用来描述三代夸克间的混合）。对于$CP$破坏的研究来说，除了弱相角之外，强相角也是非常重要的，该相角主要来源于QCD圈图的修正和理论唯象模型。 近些年来随着实验测量数据的日益增多，$B$介子三体衰变的研究成为了热门课题，人们试图采用不同的理论模型来解释实验的相关结果。本文结合LHCb和$BABAR$实验组的相关数据，运用QCD因子化的方法分别对$B^-\rightarrow K^-\pi^+\pi^-$ 衰变道和 $B^-\rightarrow \pi^-\pi^+\pi^-$衰变道的局域$CP$破坏进行了研究。对于$B^-\rightarrow K^-\pi^+\pi^-$ 衰变道，我们考虑了两种不同的情况： 第一种是考虑$f_0(500)$ 和 $\rho^0(770)$ 两个中间共振态的贡献，并加入这两个共振态的相对强相角，得出$f_0(500)$ 和$\rho^0(770)$ 共振态的干涉是可以引起实验所给出的局域$CP$破坏的；第二种是考虑了$[\pi\pi]$ 系统($\sigma(600)$, $\rho^0(770)$, $\omega(782)$)，$[K\pi]$系统($K^0(700)(\kappa)$, $K^*(892)$$K^*(1410)$, $K_0^*(1430)$, $K^*(1680)$，$K_2^*(1430)$)以及非共振态的贡献，同时考虑了$\rho-\omega$混合机制，假设各个共振态之间以及它们与非共振态之间的相对强相角为零。我们发现共振态与非共振态的干涉可以引起实验上的$CP$破坏结果。除此之外，我们发现对于$B^-\rightarrow K^-\pi^+\pi^-$ 衰变道的局域$CP$ 破坏，$[\pi\pi]$ 共振态的贡献要分别大于$[K\pi]$ 和非共振态的贡献。分别将第一、第二两种情况下的局域$CP$破坏理论结果与实验结果相匹配，可得到$B\rightarrow SP$ 衰变道端点发散的参数$\rho_S$ 和$\phi_S$。 运用这对参数我们预言了$B^-\rightarrow K^-f_0(500)$衰变道的$CP$ 破坏和衰变分支比。 对于 $B^-\rightarrow \pi^-\pi^+\pi^-$ 衰变道我们考虑了$\sigma(600)$ 和$\rho^0(770)$ 中间共振态和非共振态的贡献。同样地将我们的理论与实验结果进行匹配得到$B\rightarrow SP$ 衰变道端点发散的参数，并得出共振态与非共振态的干涉是可以引起实验给出的$B^-\rightarrow \pi^-\pi^+\pi^-$衰变道的局域$CP$ 破坏的。在对$B^-\rightarrow K^-\pi^+\pi^-$ 和$B^-\rightarrow \pi^-\pi^+\pi^-$这两个衰变道的研究中，我们发现得到的$\rho_S$ 要比传统的约束$\rho\leq1$ 大，较大的$\rho_S$参数值表明硬散射部分和弱湮灭部分的共献是比较大的，在理论计算过程中这两部分的贡献是不能忽略掉的。实际上，目前也已经有实验以及理论方面的研究来证明这一结论。 与矢量介子和张量介子相关性质研究相对比，标量介子的研究是一个长期存在的难题，最主要的一个原因就是标量介子的宽度非常的宽，这样一来就会导致共振态和实验本底产生非常强的重合现象，不利于相关实验的进行。因此到目前为止含有标量介子衰变道的研究是相对较少的。在理论方面，尽管QCD 理论取得了显著的成功, 但是在解释轻的标量介子的结构组成上还是存在争议的。理论学家试图用不同的理论模型来解释轻的标量介子的构成，例如两夸克态、四夸克态、介子-介子束缚态甚至还包括标量胶球。在本文中，我们采用两夸克模型再结合$f_0(980)$介子和$f_0(500)$介子的混合来研究$f_0(500)$介子的相关衰变道。

In recent years, prompted by a large number of experimental measurements, three-body hadronic $B$ meson decays have been studied by using different theoretical frameworks. In our work, with the related data of the LHCb Collaboration and the BABAR Collaboration, we study the localized $CP$ violations in $B^-\rightarrow K^-\pi^+\pi^-$ decay and the $B^-\rightarrow \pi^-\pi^+\pi^-$ decay, respectively, within the framework of the QCD factorization approach. As for the $B^-\rightarrow K^-\pi^+\pi^-$ decay, we consider two different situations with different intermediate resonances. Firstly, we consider the $f_0(500)$ and $\rho^0(770)$ resonances including their relative strong phase. From our calculation, one can get the interference of the $f_0(500)$ and $\rho^0(770)$ indeed induce the data for the localized CP violation in the $B^-\rightarrow K^-\pi^+\pi^-$ decay. Secondly, both the resonance and the nonresonance contributions are studied for the $B^-\rightarrow K^-\pi^+\pi^-$ decay. The resonance contributions include those not only from $[\pi\pi]$ channels including $\sigma(600)$, $\rho^0(770)$ and $\omega(782)$ but also from $[K\pi]$ channels including $K_0^*(700)(\kappa)$, $K^*(892)$, $K_0^*(1430)$, $K^*(1410)$, $K^*(1680)$ and $K_2^*(1430)$, and we also consider the $\rho-\omega$ mixing. The relative strong phases between the resonances or between the resonance and nonresonance will be set to zero for simplicity. One can get the interference of the resonance and the nonresonance can induce the experimental localized CP violation in the $B^-\rightarrow K^-\pi^+\pi^-$ decay. Comparing our results, we can find the contribution from the $[\pi\pi]$ resonances are much larger than that from the $[K\pi]$ resonances and nonresonance. By fitting the experimental localized CP violation data in two different situations, respectively, we obtain the divergence parameters $\rho_S$ and $\phi_S$ of the $B\rightarrow SP$ decay. With the regions of these two parameters, we predict the $CP$ violation and the branching fraction for $B^-\rightarrow K^-f_0(500)$ decay mode. For the $B^-\rightarrow \pi^-\pi^+\pi^-$ decay, we consider the contributions from the $\sigma(600)$ and $\rho^0(770)$ resonances and the nonresonance. We also obtain the exist of the divergence parameters $\rho_S$ and $\phi_S$ of the $B\rightarrow SP$ decay, it reveal that the interference of the resonance and the nonresonance can induce the experimental localized CP violation in this decay. From our studies of these two decays, we find $\rho_S$ (one of the end-point divergence parameters) of the $B\rightarrow SP$ is larger than the traditional constraint $\rho\leq1$. Large values of $\rho_S$ reveal that the contributions from the weak annihilation and the hard spectator scattering processes are both large, the contributions from the weak annihilation and the hard spectator scattering should not be neglected. In fact, the large contributions from these two parts have been observed and predicted in experimental and theoretical studies. In contrast to vector and tensor mesons, the identification of scalar mesons is a long-standing puzzle, because some of them have large decay widths which cause strong overlaps between resonances and backgrounds in experiments. There are few experiments to study the decays including the scalar mesons. In spite of the striking success of QCD theory, the underlying structure of the light scalar mesons is still under controversy, scalar mesons have been identified as ordinary $\bar{q}q$ states, four-quark states, or meson-meson bound states, or even those supplemented with a scalar glueball, in our work we will follow the $\bar{q}q$ quark model and mixing with $f_0(980)$ for $f_0(500)$ meson.