Enhanced Direct CP Violation in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$

Abstract

We study direct CP violation in the hadronic decay $B^{\pm }\to {\rho }^0{\pi }^{\pm }$, including the effect of $\rho -\omega$ mixing. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements, especially the Wolfenstein parameter $\eta$. For fixed $N_c$ (the effective parameter associated with factorization), the CP violating asymmetry, $a$, has a maximum of order $30$ when the invariant mass of the ${\pi }^{+}{\pi }^{-}$ pair is in the vicinity of the $\omega$ resonance. The sensitivity of the asymmetry, $a$, to $N_c$ is small. Moreover, if $N_c$ is constrained using the latest experimental branching ratios from the CLEO collaboration, we find that the sign of $\sin \delta$ is always positive. Thus, a measurement of direct CP violation in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$ would remove the mod$(\pi )$ ambiguity in $\arg [-\frac{V_{td}{V}_{tb}^{\star }}{V_{ud}{V}_{ub}^{\star }}]$.

Comments: 37 pages, 7 figures