  The Standard Model constraints on alpha which can be derived from the B->
pipi decays are revisited in some depth. As experimental inputs, the three
branching ratios, the two CP parameters Spipi and Cpipi 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 B00 and the
function C00(B00) are introduced. The Grossman-Quinn bound is rediscussed. A
close form expression is given for alpha as a function of the measurements.
Various scenarii for the future of the isospin analysis are explored. To probe
the Standard Model the (B00,C00) plane is introduced.
