How isospin violation mocks open-quotes newclose quotes physics: π0-η,η' mixing in B→ππ decays

An isospin analysis of B→ππ decays yields sin; 2α, where α ≡ arg[- Vtd Vtb*/(Vud Vub*)] and Vij is a CKM matrix element, without hadronic uncertainty if isospin is a perfect symmetry. Isospin, however, is broken not only by electroweak effects but also by the u and d quark mass difference. The latter drives π0-η,η' mixing and converts the isospin-perfect triangle relation between the B→ππ amplitudes to a quadrilateral. The combined isospin-violating effects impact the extracted value of sin; 2α in a significant manner, particularly if the latter is small. copyright 1999 The American Physical Society