Hunting for direct CP violation in ${\bar{B}}_s^0\to {\pi }^{+}{\pi }^{-}{K}^{\ast 0}$

Abstract

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