MeasuringαinB(t)→ρ±π∓

Defining a most economical parametrization of time-dependent $B\to {\rho }^{\pm }{\pi }^{\mp }$ decays, including a measurable phase ${\alpha }_{\mathrm{e}\mathrm{f}\mathrm{f}}$ which equals the weak phase $\alpha$ in the limit of vanishing penguin amplitudes, we propose two ways for determining $\alpha$ in this processes. We explain the limitation of one method, assuming only that two relevant tree amplitudes factorize and that their relative strong phase ${\delta }_t$ is negligible. The other method, based on broken flavor SU(3), permits a determination of $\alpha$ in $B^0\to {\rho }^{\pm }{\pi }^{\mp }$ in an overconstrained system using also rate measurements of $B^{0,+}\to K^{*}\pi$ and $B^{0,+}\to \rho K$. Current data are shown to restrict two ratios of penguin and tree amplitudes $r_{\pm }$ to a narrow range around 0.2 and to imply an upper bound $|{\alpha }_{\mathrm{e}\mathrm{f}\mathrm{f}}-\alpha |<15°$. Assuming that ${\delta }_t$ is much smaller than 90°, we find $\alpha =(93\pm 16)°$ and $(102\pm 20)°$ using BABAR and BELLE results for $B(t)\to {\rho }^{\pm }{\pi }^{\mp }$. Avoiding this assumption for completeness, we demonstrate the reduction of discrete ambiguities in $\alpha$ with increased statistics and show that SU(3) breaking effects are effectively second order in $r_{\pm }$.