Isospin constraints from/on B $\to \pi \pi$

The standard model constraints on alpha which can be derived from the B to pi pi decays are revisited in some depth. As experimental inputs, the B/sup 0/ to pi /sup +/ pi /sup -/, B/sup +/ to pi /sup +/ pi /sup 0/ decays complemented by the B/sup 0/ to pi /sup 0/ pi /sup 0/ decays, the CP parameters S/sub pi pi / and C/sub pi pi /, and/or the value of alpha 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 B/sup 00/ and the function C/sub 00/(B/sup 00/) are introduced. While another bound applied to BABAR results is shown to imply that cos(2 alpha /sub eff/) is negative. The Grossman- Quinn bound is rediscussed. A close form expression is given for alpha as a function of the measurements. Various scenarios for the future of the isospin analysis are explored. To probe the standard model the (B/sup 00/, C/sub 00/) plane is introduced.