Hunting for direct CP violation in $\bar{B}_s^0 \to {π^+}{π^-}K^{*0}$
In perturbative QCD approach, based on the first order of isospin symmetry breaking, we study the direct $CP$ violation in the decay of $\bar{B}_s^0\toρ(ω)K^{*0}\to {π^+}{π^-}K^{*0}$. An interesting mechanism is applied to enlarge the $CP$ violating asymmetry involving the charge symmetry breaking between $ρ$ and $ω$. We find that the $CP$ violation is large by the $ρ-ω$ mixing mechanism when the invariant masses of the $π^+π^-$ pairs is in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\toρ(ω)K^{*0}\to{π^+}{π^-}K^{*0}$, the maximum $CP$ violation can reach $-59.12\%$. Furthermore, taking $ρ-ω$ mixing into account, we calculate the branching ratio for $\bar{B}_s^0 \rightarrow ρ(ω) K^{*0}$. We also discuss the possibility of observing the predicted $CP$ violation asymmetry at the LHC.