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In this work, we study the localized $CP$ violation and the branchingfraction of the four-body decay $\bar{B}^0\rightarrow K^-\pi^+\pi^-\pi^+$ byemploying a quasi-two-body QCD factorization approach. Considering theinterference of $\bar{B}^0\rightarrow \bar{K}_0^*(700)\rho^0(770)\rightarrowK^-\pi^+\pi^-\pi^+$ and $\bar{B}^0\rightarrow \bar{K}^*(892)f_0(500)\rightarrowK^-\pi^+\pi^-\pi^+$ channels, we predict $\mathcal{A_{CP}}(\bar{B}^0\rightarrowK^-\pi^+\pi^-\pi^+)\in[0.15,0.28]$ and $\mathcal{B}(\bar{B}^0\rightarrowK^-\pi^+\pi^-\pi^+)\in[1.73,5.10]\times10^{-7}$, respectively, which shows thatthis two channels' interference mechanism can induce the localized $CP$violation to this four-body decay. Meanwhile, within the two quark modelframework for the scalar mesons $f_0(500)$ and $\bar{K}_0^*(700)$, we calculatethe direct CP violations and branching fractions of the $\bar{B}^0\rightarrow\bar{K}_0^*(700)\rho^0(770)$ and $\bar{B}^0\rightarrow \bar{K}^*(892)f_0(500)$decays, respectively. The corresponding results are$\mathcal{A_{CP}}(\bar{B}^0\rightarrow \bar{K}_0^*(700)\rho^0(770)) \in [0.20,0.36]$, $\mathcal{A_{CP}}(\bar{B}^0\rightarrow \bar{K}^*(892)f_0(500))\in[0.08, 0.12]$, $\mathcal{B} (\bar{B}^0\rightarrow\bar{K}_0^*(700)\rho^0(770)\in [6.76, 18.93]\times10^{-8}$ and $\mathcal{B}(\bar{B}^0\rightarrow \bar{K}^*(892)f_0(500))\in [2.66, 4.80]\times10^{-6}$,respectively, indicating the $CP$ violations of these two two-body decays areboth positive and the branching fractions are quite different. These studiesprovide a new way to investigate the aforementioned four-body decay and couldbe helpful in clarifying the configuration of the structure of light scalarmeson.

Studying the localized $CP$ violation and the branching fraction of the $\bar{B}^0\rightarrow K^-\pi^+\pi^+\pi^-$ decay