Within the quasi-two-body decay model, we study the localized $CP$ violation and branching fraction of the four-body decay $\bar{ B}^0\rightarrow [K^-\pi^+]_{ S/V}[\pi^+\pi^-]_{ V/S} \rightarrow K^-\pi^+\pi^-\pi^+$ when $K^-\pi^+$ and $\pi^-\pi^+$ pair invariant masses are $0.35<m_{ K^-\pi^+}<2.04 \, \mathrm{ GeV}$ and $0<m_{ \pi^-\pi^+}<1.06\, \mathrm{ GeV}$, with the pairs being dominated by the $\bar{ K}^*_0(700)^0$, $\bar{ K}^*(892)^0$, $\bar{ K}^*(1410)^0$, $\bar{ K}^*_0(1430)$ and $\bar{ K}^*(1680)^0$, and $f_0(500)$, $\rho^0(770)$ , $\omega(782)$ and $f_0(980)$ resonances, respectively. When dealing with the dynamical functions of these resonances, $f_0(500)$, $\rho^0(770)$, $f_0(980)$ and $\bar{ K}^*_0(1430)$ are modeled with the Bugg model, Gounaris-Sakurai function, Flatt$\acute{ \mathrm{ e}}$ formalism and LASS lineshape, respectively, while others are described by the relativistic Breit-Wigner function. Adopting the end point divergence parameters $\rho_A\in[0,0.5]$ and $\phi_A\in[0,2\pi]$, our predicted results are $\mathcal{ A_{ CP}}(\bar{ B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in[-0.383,0.421]$ and $\mathcal{ B}(\bar{ B}^0\rightarrow K^-\pi^+\pi^+\pi^-)\in[7.36,199.69]\times10^{ -8}$ based on the hypothetical $q\bar{ q}$ structures for the scalar mesons in the QCD factorization approach. Meanwhile, we calculate the $CP$ violating asymmetries and branching fractions of the two-body decays $\bar{ B}^0\rightarrow SV(VS)$ and all the individual four-body decays $\bar{ B}^0\rightarrow SV(VS) \rightarrow K^-\pi^+\pi^-\pi^+$, respectively. Our theoretical results for the two-body decays $\bar{ B}^0\rightarrow \bar{ K}^*(892)^0$$f_0(980)$, $\bar{ B}^0\rightarrow \bar{ K}^*_0(1430)^0$$\omega(782)$, $\bar{ B}^0\rightarrow \bar{ K}^*(892)^0f_0(980)$, $\bar{ B}^0\rightarrow\bar{ K}^*_0(1430)^0\rho$,
Categories: hep-ph