Direct CP violation in B \to \rho^0(\omega) PS

Abstract

We calculate the direct CP violating asymmetry parameter, $a_{CP}$, for $B\to {\pi }^{+}{\pi }^{-}\pi$ and $B\to {\pi }^{+}{\pi }^{-}K$ decays, in the case where ${\rho }^0-\omega$ mixing effects are taken into account. We find that the direct CP asymmetry for $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$, ${\bar{B}}^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$, $B^{-}\to {\pi }^{+}{\pi }^{-}{K}^{-}$ and ${\bar{B}}^0\to {\pi }^{+}{\pi }^{-}{\bar{K}}^0$, reaches its maximum when the invariant mass ${\pi }^{+}{\pi }^{-}$ is in the vicinity of the $\omega$ meson mass. The inclusion of ${\rho }^0-\omega$ mixing provides an opportunity to erase, without ambiguity, the phase uncertainty mod$(\pi )$ in the determination of the CKM angles $\alpha$ in case of $b\to u$ and $\gamma$ in case of $b\to s$.

Comments: 5 pages, 1 figure. Talk given at the International Europhysics Conference on High Energy Physics, July 21st - 27th 2005, Lisboa, Portugal