The Standard Model constraints on \documentclass[12pt]{minimal}
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\begin{document}$\alpha$\end{document} which can be derived from the \documentclass[12pt]{minimal}
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\begin{document}$B\rightarrow\pi\pi$\end{document} decays are revisited in some depth. As experimental inputs, the \documentclass[12pt]{minimal}
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\begin{document}$B^0\rightarrow\pi^ + \pi^-$\end{document}, \documentclass[12pt]{minimal}
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\begin{document}$B^ + \rightarrow\pi^ + \pi^0$\end{document} decays complemented by the \documentclass[12pt]{minimal}
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\begin{document}$B^0\rightarrow\pi^0\pi^0$\end{document} decays, the CP parameters \documentclass[12pt]{minimal}
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\begin{document}$S_{\pi\pi}$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$C_{\pi\pi}$\end{document}, and/or the value of \documentclass[12pt]{minimal}
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\begin{document}$\alpha$\end{document} as determined by the global CKM fit are used. The constraints discussed here are model independent in the sense that they rely only on Isospin symmetry, following the Gronau-London proposal. A new bound on \documentclass[12pt]{minimal}
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\begin{document}$\mathcal{B}^{00}$\end{document} and the function \documentclass[12pt]{minimal}
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\begin{document}$C_{00}(\mathcal{B}^{00})$\end{document} are introduced. While another bound applied to BABAR results is shown to imply that \documentclass[12pt]{minimal}
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\begin{document}$\cos(2\alpha_{\rm eff})$\end{document} is negative. The Grossman-Quinn bound is rediscussed. A close form expression is given for \documentclass[12pt]{minimal}
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\begin{document}$\alpha$\end{document} as a function of the measurements. Various scenarios for the future of the isospin analysis are explored. To probe the Standard Model the \documentclass[12pt]{minimal}
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\begin{document}$(\mathcal{B}^{00},C_{00})$\end{document} plane is introduced.
