Enhanced directCPviolation inB±→ρ0π±

We study direct $\mathrm{CP}$ violation in the hadronic decay $B^{\pm }\to {\rho }^0{\pi }^{\pm },$ including the effect of $\rho -\omega$ mixing. We find that the $\mathrm{CP}$ 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 $\mathrm{CP}$ violating asymmetry a has a maximum of order 30%–50% 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 $\mathrm{CP}$ violation in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$ would remove the $\mathrm{mod}\left(\pi \right)$ ambiguity in $\arg \left[-\right[V_{\mathrm{td}}{V}_{\mathrm{tb}}^{\star }{/V}_{\mathrm{ud}}{V}_{\mathrm{ub}}^{\star }].$