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Enhanced Direct CP Violation in $B^{\pm} \to ρ^{0} π^{\pm}$

We study direct CP violation in the hadronic decay $B^{\pm} \to ρ^{0}π^{\pm}$, including the effect of $ρ- ω$ mixing. We find that the CP violating asymmetry is strongly dependent on the CKM matrix elements, especially the Wolfenstein parameter $η$. For fixed $N_{c}$ (the effective parameter associated with factorization), the CP violating asymmetry, $a$, has a maximum of order $30%-50%$ when the invariant mass of the $π^{+}π^{-}$ pair is in the vicinity of the $ω$ 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 $\sin δ$ is always positive. Thus, a measurement of direct CP violation in $B^{\pm} \to ρ^{0}π^{\pm}$ would remove the mod$(π)$ ambiguity in ${\rm arg}[ - \frac{V_{td}V_{tb}^{\star}}{V_{ud}V_{ub}^{\star}}]$.