Comprehensive Study of $\overline B^0\to K^0(\overline K^0) K^\mp\pi^\pm$ Decays in the Factorization Approach

Using the factorization approach, we investigate the $\overline B^0 \to \overline K^0K^+\pi^-$ and $\overline B^0 \to K^0K^-\pi^+$ decays individually including the resonant and nonresonant contributions. Under the flavor SU(3) symmetry, we obtain the total branching fraction $BR [\overline B^0 \to (\overline K^0K^+\pi^-+K^0K^-\pi^+)]=(7.17^{+0.50+1.97+0.08}_{-0.53-1.42-0.07})\times 10^{-6}$, which is in agreement with the recent measurements of BaBar and LHCb within errors. For the decay $\overline B^0 \to \overline K^0K^+\pi^-$, the nonresonant background and $a_0^+(1450)$ pole in the current-induced process provide large contribution, the latter of which has not been included in previous studies. On the contrary,the decay $\overline B^0 \to K^0K^-\pi^+$ is dominated by the nonresonant background and the offshell $\rho^-$ pole. When the flavor SU(3) symmetry breaking and the final-state rescattering are considered under two different scenarios, the results can also accommodate the experimental data with large uncertainties. Moreover, the direct $CP$ asymmetry of $\overline B^0 \to \overline K^0K^+\pi^-$ is found to be sensitive to the matrix element of scalar density. These predictions could be further tested in the LHCb experiment or Super-b factory in future.