$CP$ violation for $B_c^{+}\to D_{(s)}^{+}{\pi }^{+}{\pi }^{-}$ in Perturbative QCD

Abstract

In the perturbative QCD (PQCD) approach we study the direct $CP$ violation in $B_c^{+}\to D_{(s)}^{+}{\rho }^0(\omega )\to D_{(s)}^{+}{\pi }^{+}{\pi }^{-}$ via the $\rho -\omega$ mixing mechanism. We find that the $CP$ violation can be enhanced by $\rho -\omega$ mixing when the invariant masses of the ${\pi }^{+}{\pi }^{-}$ pairs are in the vicinity of the $\omega$ resonance. For the decay process $B_c^{+}\to D^{+}{\rho }^0(\omega )\to D^{+}{\pi }^{+}{\pi }^{-}$, the maximum $CP$ violation can reach 7.5 {\%}.

Comments: arXiv admin note: text overlap with arXiv:1112.1257, arXiv:0704.3132 by other authors